What is the general solution for 2sin^{23}(x)+sin^{26}(x)-2=0 ?

The general solution for 2sin^{23}(x)+sin^{26}(x)-2=0 is x=1.38743…+2pin,x=pi-1.38743…+2pin

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2sin^{23}(x)+sin^{26}(x)-2=0

Solution

2 sin^{23} (x) + sin^{26} (x) - 2 = 0

Solution

x = 1.38743 \dots + 2 πn, x = π - 1.38743 \dots + 2 πn

Degrees

x = 79.49402 \dots^{\circ} + 36 0^{\circ} n, x = 100.50597 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 sin^{23} (x) + sin^{26} (x) - 2 = 0

Rewrite using trig identities

- 2 + sin^{26} (x) + 2 sin^{23} (x)

Use the basic trigonometric identity:

sin (x) = \frac{1}{csc ( x )}

= - 2 + (\frac{1}{csc ( x )})^{26} + 2 (\frac{1}{csc ( x )})^{23}

Simplify

- 2 + (\frac{1}{csc ( x )})^{26} + 2 (\frac{1}{csc ( x )})^{23} : - 2 + \frac{1}{csc ^{26} ( x )} + \frac{2}{csc ^{23} ( x )}

- 2 + (\frac{1}{csc ( x )})^{26} + 2 (\frac{1}{csc ( x )})^{23}

(\frac{1}{csc ( x )})^{26} = \frac{1}{csc ^{26} ( x )}

(\frac{1}{csc ( x )})^{26}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{26}}{csc ^{26} ( x )}

Apply rule

1^{a} = 1

1^{26} = 1

= \frac{1}{csc ^{26} ( x )}

2 (\frac{1}{csc ( x )})^{23} = \frac{2}{csc ^{23} ( x )}

2 (\frac{1}{csc ( x )})^{23}

(\frac{1}{csc ( x )})^{23} = \frac{1}{csc ^{23} ( x )}

(\frac{1}{csc ( x )})^{23}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{23}}{csc ^{23} ( x )}

Apply rule

1^{a} = 1

1^{23} = 1

= \frac{1}{csc ^{23} ( x )}

= 2 \cdot \frac{1}{csc ^{23} ( x )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{csc ^{23} ( x )}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2}{csc ^{23} ( x )}

= - 2 + \frac{1}{csc ^{26} ( x )} + \frac{2}{csc ^{23} ( x )}

= - 2 + \frac{1}{csc ^{26} ( x )} + \frac{2}{csc ^{23} ( x )}

- 2 + \frac{1}{csc ^{26} ( x )} + \frac{2}{csc ^{23} ( x )} = 0

Solve by substitution

- 2 + \frac{1}{csc ^{26} ( x )} + \frac{2}{csc ^{23} ( x )} = 0

Let:

csc (x) = u

- 2 + \frac{1}{u ^{26}} + \frac{2}{u ^{23}} = 0

- 2 + \frac{1}{u ^{26}} + \frac{2}{u ^{23}} = 0 : u \approx 1.01704 \dots, u \approx - 0.79244 \dots

- 2 + \frac{1}{u ^{26}} + \frac{2}{u ^{23}} = 0

Multiply by LCM

- 2 + \frac{1}{u ^{26}} + \frac{2}{u ^{23}} = 0

Find Least Common Multiplier of

u^{26}, u^{23} : u^{26}

u^{26}, u^{23}

Lowest Common Multiplier (LCM)

Compute an expression comprised of factors that appear either in

u^{26}

u^{23}

= u^{26}

Multiply by LCM=

u^{26}

- 2 u^{26} + \frac{1}{u ^{26}} u^{26} + \frac{2}{u ^{23}} u^{26} = 0 \cdot u^{26}

Simplify

- 2 u^{26} + \frac{1}{u ^{26}} u^{26} + \frac{2}{u ^{23}} u^{26} = 0 \cdot u^{26}

Simplify

\frac{1}{u ^{26}} u^{26} : 1

\frac{1}{u ^{26}} u^{26}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot u ^{26}}{u ^{26}}

Cancel the common factor:

u^{26}

= 1

Simplify

\frac{2}{u ^{23}} u^{26} : 2 u^{3}

\frac{2}{u ^{23}} u^{26}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 u ^{26}}{u ^{23}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{u ^{26}}{u ^{23}} = u^{26 - 23}

= 2 u^{26 - 23}

Subtract the numbers:

26 - 23 = 3

= 2 u^{3}

Simplify

0 \cdot u^{26} : 0

0 \cdot u^{26}

Apply rule

0 \cdot a = 0

= 0

- 2 u^{26} + 1 + 2 u^{3} = 0

- 2 u^{26} + 1 + 2 u^{3} = 0

- 2 u^{26} + 1 + 2 u^{3} = 0

Solve

- 2 u^{26} + 1 + 2 u^{3} = 0 : u \approx 1.01704 \dots, u \approx - 0.79244 \dots

- 2 u^{26} + 1 + 2 u^{3} = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 2 u^{26} + 2 u^{3} + 1 = 0

Find one solution for

- 2 u^{26} + 2 u^{3} + 1 = 0

using Newton-Raphson:

u \approx 1.01704 \dots

- 2 u^{26} + 2 u^{3} + 1 = 0

Newton-Raphson Approximation Definition

f (u) = - 2 u^{26} + 2 u^{3} + 1

Find

f^{^{'}} (u) : - 52 u^{25} + 6 u^{2}

\frac{d}{d u} (- 2 u^{26} + 2 u^{3} + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d u} (2 u^{26}) + \frac{d}{d u} (2 u^{3}) + \frac{d}{d u} (1)

\frac{d}{d u} (2 u^{26}) = 52 u^{25}

\frac{d}{d u} (2 u^{26})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d u} (u^{26})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 2 \cdot 26 u^{26 - 1}

Simplify

= 52 u^{25}

\frac{d}{d u} (2 u^{3}) = 6 u^{2}

\frac{d}{d u} (2 u^{3})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d u} (u^{3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 2 \cdot 3 u^{3 - 1}

Simplify

= 6 u^{2}

\frac{d}{d u} (1) = 0

\frac{d}{d u} (1)

Derivative of a constant:

\frac{d}{d x} (a) = 0

= 0

= - 52 u^{25} + 6 u^{2} + 0

Simplify

= - 52 u^{25} + 6 u^{2}

Let

u_{0} = 1

Compute

u_{n + 1}

until

Δ u_{n + 1} < 0.000001

u_{1} = 1.02173 \dots : Δ u_{1} = 0.02173 \dots

f (u_{0}) = - 2 \cdot 1^{26} + 2 \cdot 1^{3} + 1 = 1

f^{^{'}} (u_{0}) = - 52 \cdot 1^{25} + 6 \cdot 1^{2} = - 46

u_{1} = 1.02173 \dots

Δ u_{1} = ∣ 1.02173 \dots - 1 ∣ = 0.02173 \dots

Δ u_{1} = 0.02173 \dots

u_{2} = 1.01732 \dots : Δ u_{2} = 0.00441 \dots

f (u_{1}) = - 2 \cdot 1.02173 \dots^{26} + 2 \cdot 1.02173 \dots^{3} + 1 = - 0.36511 \dots

f^{^{'}} (u_{1}) = - 52 \cdot 1.02173 \dots^{25} + 6 \cdot 1.02173 \dots^{2} = - 82.75965 \dots

u_{2} = 1.01732 \dots

Δ u_{2} = ∣ 1.01732 \dots - 1.02173 \dots ∣ = 0.00441 \dots

Δ u_{2} = 0.00441 \dots

u_{3} = 1.01705 \dots : Δ u_{3} = 0.00027 \dots

f (u_{2}) = - 2 \cdot 1.01732 \dots^{26} + 2 \cdot 1.01732 \dots^{3} + 1 = - 0.02036 \dots

f^{^{'}} (u_{2}) = - 52 \cdot 1.01732 \dots^{25} + 6 \cdot 1.01732 \dots^{2} = - 73.68555 \dots

u_{3} = 1.01705 \dots

Δ u_{3} = ∣ 1.01705 \dots - 1.01732 \dots ∣ = 0.00027 \dots

Δ u_{3} = 0.00027 \dots

u_{4} = 1.01704 \dots : Δ u_{4} = 1.01651 E - 6

f (u_{3}) = - 2 \cdot 1.01705 \dots^{26} + 2 \cdot 1.01705 \dots^{3} + 1 = - 0.00007 \dots

f^{^{'}} (u_{3}) = - 52 \cdot 1.01705 \dots^{25} + 6 \cdot 1.01705 \dots^{2} = - 73.14807 \dots

u_{4} = 1.01704 \dots

Δ u_{4} = ∣ 1.01704 \dots - 1.01705 \dots ∣ = 1.01651 E - 6

Δ u_{4} = 1.01651 E - 6

u_{5} = 1.01704 \dots : Δ u_{5} = 1.36911 E - 11

f (u_{4}) = - 2 \cdot 1.01704 \dots^{26} + 2 \cdot 1.01704 \dots^{3} + 1 = - 1.00145 E - 9

f^{^{'}} (u_{4}) = - 52 \cdot 1.01704 \dots^{25} + 6 \cdot 1.01704 \dots^{2} = - 73.14609 \dots

u_{5} = 1.01704 \dots

Δ u_{5} = ∣ 1.01704 \dots - 1.01704 \dots ∣ = 1.36911 E - 11

Δ u_{5} = 1.36911 E - 11

u \approx 1.01704 \dots

Apply long division:

\frac{- 2 u ^{26} + 2 u ^{3} + 1}{u - 1.01704 \dots} = - 2 u^{25} - 2.03409 \dots u^{24} - 2.06878 \dots u^{23} - 2.10405 \dots u^{22} - 2.13992 \dots u^{21} - 2.17641 \dots u^{20} - 2.21352 \dots u^{19} - 2.25126 \dots u^{18} - 2.28964 \dots u^{17} - 2.32868 \dots u^{16} - 2.36838 \dots u^{15} - 2.40876 \dots u^{14} - 2.44983 \dots u^{13} - 2.49160 \dots u^{12} - 2.53408 \dots u^{11} - 2.57729 \dots u^{10} - 2.62123 \dots u^{9} - 2.66592 \dots u^{8} - 2.71138 \dots u^{7} - 2.75761 \dots u^{6} - 2.80462 \dots u^{5} - 2.85244 \dots u^{4} - 2.90108 \dots u^{3} - 0.95054 \dots u^{2} - 0.96675 \dots u - 0.98323 \dots

- 2 u^{25} - 2.03409 \dots u^{24} - 2.06878 \dots u^{23} - 2.10405 \dots u^{22} - 2.13992 \dots u^{21} - 2.17641 \dots u^{20} - 2.21352 \dots u^{19} - 2.25126 \dots u^{18} - 2.28964 \dots u^{17} - 2.32868 \dots u^{16} - 2.36838 \dots u^{15} - 2.40876 \dots u^{14} - 2.44983 \dots u^{13} - 2.49160 \dots u^{12} - 2.53408 \dots u^{11} - 2.57729 \dots u^{10} - 2.62123 \dots u^{9} - 2.66592 \dots u^{8} - 2.71138 \dots u^{7} - 2.75761 \dots u^{6} - 2.80462 \dots u^{5} - 2.85244 \dots u^{4} - 2.90108 \dots u^{3} - 0.95054 \dots u^{2} - 0.96675 \dots u - 0.98323 \dots \approx 0

Find one solution for

- 2 u^{25} - 2.03409 \dots u^{24} - 2.06878 \dots u^{23} - 2.10405 \dots u^{22} - 2.13992 \dots u^{21} - 2.17641 \dots u^{20} - 2.21352 \dots u^{19} - 2.25126 \dots u^{18} - 2.28964 \dots u^{17} - 2.32868 \dots u^{16} - 2.36838 \dots u^{15} - 2.40876 \dots u^{14} - 2.44983 \dots u^{13} - 2.49160 \dots u^{12} - 2.53408 \dots u^{11} - 2.57729 \dots u^{10} - 2.62123 \dots u^{9} - 2.66592 \dots u^{8} - 2.71138 \dots u^{7} - 2.75761 \dots u^{6} - 2.80462 \dots u^{5} - 2.85244 \dots u^{4} - 2.90108 \dots u^{3} - 0.95054 \dots u^{2} - 0.96675 \dots u - 0.98323 \dots = 0

using Newton-Raphson:

u \approx - 0.79244 \dots

- 2 u^{25} - 2.03409 \dots u^{24} - 2.06878 \dots u^{23} - 2.10405 \dots u^{22} - 2.13992 \dots u^{21} - 2.17641 \dots u^{20} - 2.21352 \dots u^{19} - 2.25126 \dots u^{18} - 2.28964 \dots u^{17} - 2.32868 \dots u^{16} - 2.36838 \dots u^{15} - 2.40876 \dots u^{14} - 2.44983 \dots u^{13} - 2.49160 \dots u^{12} - 2.53408 \dots u^{11} - 2.57729 \dots u^{10} - 2.62123 \dots u^{9} - 2.66592 \dots u^{8} - 2.71138 \dots u^{7} - 2.75761 \dots u^{6} - 2.80462 \dots u^{5} - 2.85244 \dots u^{4} - 2.90108 \dots u^{3} - 0.95054 \dots u^{2} - 0.96675 \dots u - 0.98323 \dots = 0

Newton-Raphson Approximation Definition

f (u) = - 2 u^{25} - 2.03409 \dots u^{24} - 2.06878 \dots u^{23} - 2.10405 \dots u^{22} - 2.13992 \dots u^{21} - 2.17641 \dots u^{20} - 2.21352 \dots u^{19} - 2.25126 \dots u^{18} - 2.28964 \dots u^{17} - 2.32868 \dots u^{16} - 2.36838 \dots u^{15} - 2.40876 \dots u^{14} - 2.44983 \dots u^{13} - 2.49160 \dots u^{12} - 2.53408 \dots u^{11} - 2.57729 \dots u^{10} - 2.62123 \dots u^{9} - 2.66592 \dots u^{8} - 2.71138 \dots u^{7} - 2.75761 \dots u^{6} - 2.80462 \dots u^{5} - 2.85244 \dots u^{4} - 2.90108 \dots u^{3} - 0.95054 \dots u^{2} - 0.96675 \dots u - 0.98323 \dots

Find

f^{^{'}} (u) : - 50 u^{24} - 48.81839 \dots u^{23} - 47.58196 \dots u^{22} - 46.28918 \dots u^{21} - 44.93848 \dots u^{20} - 43.52826 \dots u^{19} - 42.05690 \dots u^{18} - 40.52270 \dots u^{17} - 38.92397 \dots u^{16} - 37.25893 \dots u^{15} - 35.52581 \dots u^{14} - 33.72275 \dots u^{13} - 31.84789 \dots u^{12} - 29.89928 \dots u^{11} - 27.87498 \dots u^{10} - 25.77295 \dots u^{9} - 23.59114 \dots u^{8} - 21.32743 \dots u^{7} - 18.97968 \dots u^{6} - 16.54567 \dots u^{5} - 14.02314 \dots u^{4} - 11.40979 \dots u^{3} - 8.70324 \dots u^{2} - 1.90109 \dots u - 0.96675 \dots

Let

u_{0} = - 1

Compute

u_{n + 1}

until

Δ u_{n + 1} < 0.000001

u_{1} = - 0.94691 \dots : Δ u_{1} = 0.05308 \dots

f (u_{0}) = - 2 (- 1)^{25} - 2.03409 \dots (- 1)^{24} - 2.06878 \dots (- 1)^{23} - 2.10405 \dots (- 1)^{22} - 2.13992 \dots (- 1)^{21} - 2.17641 \dots (- 1)^{20} - 2.21352 \dots (- 1)^{19} - 2.25126 \dots (- 1)^{18} - 2.28964 \dots (- 1)^{17} - 2.32868 \dots (- 1)^{16} - 2.36838 \dots (- 1)^{15} - 2.40876 \dots (- 1)^{14} - 2.44983 \dots (- 1)^{13} - 2.49160 \dots (- 1)^{12} - 2.53408 \dots (- 1)^{11} - 2.57729 \dots (- 1)^{10} - 2.62123 \dots (- 1)^{9} - 2.66592 \dots (- 1)^{8} - 2.71138 \dots (- 1)^{7} - 2.75761 \dots (- 1)^{6} - 2.80462 \dots (- 1)^{5} - 2.85244 \dots (- 1)^{4} - 2.90108 \dots (- 1)^{3} - 0.95054 \dots (- 1)^{2} - 0.96675 \dots (- 1) - 0.98323 \dots = 1.48732 \dots

f^{^{'}} (u_{0}) = - 50 (- 1)^{24} - 48.81839 \dots (- 1)^{23} - 47.58196 \dots (- 1)^{22} - 46.28918 \dots (- 1)^{21} - 44.93848 \dots (- 1)^{20} - 43.52826 \dots (- 1)^{19} - 42.05690 \dots (- 1)^{18} - 40.52270 \dots (- 1)^{17} - 38.92397 \dots (- 1)^{16} - 37.25893 \dots (- 1)^{15} - 35.52581 \dots (- 1)^{14} - 33.72275 \dots (- 1)^{13} - 31.84789 \dots (- 1)^{12} - 29.89928 \dots (- 1)^{11} - 27.87498 \dots (- 1)^{10} - 25.77295 \dots (- 1)^{9} - 23.59114 \dots (- 1)^{8} - 21.32743 \dots (- 1)^{7} - 18.97968 \dots (- 1)^{6} - 16.54567 \dots (- 1)^{5} - 14.02314 \dots (- 1)^{4} - 11.40979 \dots (- 1)^{3} - 8.70324 \dots (- 1)^{2} - 1.90109 \dots (- 1) - 0.96675 \dots = - 28.01749 \dots

u_{1} = - 0.94691 \dots

Δ u_{1} = ∣ - 0.94691 \dots - (- 1) ∣ = 0.05308 \dots

Δ u_{1} = 0.05308 \dots

u_{2} = - 0.88150 \dots : Δ u_{2} = 0.06541 \dots

f (u_{1}) = - 2 (- 0.94691 \dots)^{25} - 2.03409 \dots (- 0.94691 \dots)^{24} - 2.06878 \dots (- 0.94691 \dots)^{23} - 2.10405 \dots (- 0.94691 \dots)^{22} - 2.13992 \dots (- 0.94691 \dots)^{21} - 2.17641 \dots (- 0.94691 \dots)^{20} - 2.21352 \dots (- 0.94691 \dots)^{19} - 2.25126 \dots (- 0.94691 \dots)^{18} - 2.28964 \dots (- 0.94691 \dots)^{17} - 2.32868 \dots (- 0.94691 \dots)^{16} - 2.36838 \dots (- 0.94691 \dots)^{15} - 2.40876 \dots (- 0.94691 \dots)^{14} - 2.44983 \dots (- 0.94691 \dots)^{13} - 2.49160 \dots (- 0.94691 \dots)^{12} - 2.53408 \dots (- 0.94691 \dots)^{11} - 2.57729 \dots (- 0.94691 \dots)^{10} - 2.62123 \dots (- 0.94691 \dots)^{9} - 2.66592 \dots (- 0.94691 \dots)^{8} - 2.71138 \dots (- 0.94691 \dots)^{7} - 2.75761 \dots (- 0.94691 \dots)^{6} - 2.80462 \dots (- 0.94691 \dots)^{5} - 2.85244 \dots (- 0.94691 \dots)^{4} - 2.90108 \dots (- 0.94691 \dots)^{3} - 0.95054 \dots (- 0.94691 \dots)^{2} - 0.96675 \dots (- 0.94691 \dots) - 0.98323 \dots = 0.60204 \dots

f^{^{'}} (u_{1}) = - 50 (- 0.94691 \dots)^{24} - 48.81839 \dots (- 0.94691 \dots)^{23} - 47.58196 \dots (- 0.94691 \dots)^{22} - 46.28918 \dots (- 0.94691 \dots)^{21} - 44.93848 \dots (- 0.94691 \dots)^{20} - 43.52826 \dots (- 0.94691 \dots)^{19} - 42.05690 \dots (- 0.94691 \dots)^{18} - 40.52270 \dots (- 0.94691 \dots)^{17} - 38.92397 \dots (- 0.94691 \dots)^{16} - 37.25893 \dots (- 0.94691 \dots)^{15} - 35.52581 \dots (- 0.94691 \dots)^{14} - 33.72275 \dots (- 0.94691 \dots)^{13} - 31.84789 \dots (- 0.94691 \dots)^{12} - 29.89928 \dots (- 0.94691 \dots)^{11} - 27.87498 \dots (- 0.94691 \dots)^{10} - 25.77295 \dots (- 0.94691 \dots)^{9} - 23.59114 \dots (- 0.94691 \dots)^{8} - 21.32743 \dots (- 0.94691 \dots)^{7} - 18.97968 \dots (- 0.94691 \dots)^{6} - 16.54567 \dots (- 0.94691 \dots)^{5} - 14.02314 \dots (- 0.94691 \dots)^{4} - 11.40979 \dots (- 0.94691 \dots)^{3} - 8.70324 \dots (- 0.94691 \dots)^{2} - 1.90109 \dots (- 0.94691 \dots) - 0.96675 \dots = - 9.20354 \dots

u_{2} = - 0.88150 \dots

Δ u_{2} = ∣ - 0.88150 \dots - (- 0.94691 \dots) ∣ = 0.06541 \dots

Δ u_{2} = 0.06541 \dots

u_{3} = - 0.81453 \dots : Δ u_{3} = 0.06696 \dots

f (u_{2}) = - 2 (- 0.88150 \dots)^{25} - 2.03409 \dots (- 0.88150 \dots)^{24} - 2.06878 \dots (- 0.88150 \dots)^{23} - 2.10405 \dots (- 0.88150 \dots)^{22} - 2.13992 \dots (- 0.88150 \dots)^{21} - 2.17641 \dots (- 0.88150 \dots)^{20} - 2.21352 \dots (- 0.88150 \dots)^{19} - 2.25126 \dots (- 0.88150 \dots)^{18} - 2.28964 \dots (- 0.88150 \dots)^{17} - 2.32868 \dots (- 0.88150 \dots)^{16} - 2.36838 \dots (- 0.88150 \dots)^{15} - 2.40876 \dots (- 0.88150 \dots)^{14} - 2.44983 \dots (- 0.88150 \dots)^{13} - 2.49160 \dots (- 0.88150 \dots)^{12} - 2.53408 \dots (- 0.88150 \dots)^{11} - 2.57729 \dots (- 0.88150 \dots)^{10} - 2.62123 \dots (- 0.88150 \dots)^{9} - 2.66592 \dots (- 0.88150 \dots)^{8} - 2.71138 \dots (- 0.88150 \dots)^{7} - 2.75761 \dots (- 0.88150 \dots)^{6} - 2.80462 \dots (- 0.88150 \dots)^{5} - 2.85244 \dots (- 0.88150 \dots)^{4} - 2.90108 \dots (- 0.88150 \dots)^{3} - 0.95054 \dots (- 0.88150 \dots)^{2} - 0.96675 \dots (- 0.88150 \dots) - 0.98323 \dots = 0.23451 \dots

f^{^{'}} (u_{2}) = - 50 (- 0.88150 \dots)^{24} - 48.81839 \dots (- 0.88150 \dots)^{23} - 47.58196 \dots (- 0.88150 \dots)^{22} - 46.28918 \dots (- 0.88150 \dots)^{21} - 44.93848 \dots (- 0.88150 \dots)^{20} - 43.52826 \dots (- 0.88150 \dots)^{19} - 42.05690 \dots (- 0.88150 \dots)^{18} - 40.52270 \dots (- 0.88150 \dots)^{17} - 38.92397 \dots (- 0.88150 \dots)^{16} - 37.25893 \dots (- 0.88150 \dots)^{15} - 35.52581 \dots (- 0.88150 \dots)^{14} - 33.72275 \dots (- 0.88150 \dots)^{13} - 31.84789 \dots (- 0.88150 \dots)^{12} - 29.89928 \dots (- 0.88150 \dots)^{11} - 27.87498 \dots (- 0.88150 \dots)^{10} - 25.77295 \dots (- 0.88150 \dots)^{9} - 23.59114 \dots (- 0.88150 \dots)^{8} - 21.32743 \dots (- 0.88150 \dots)^{7} - 18.97968 \dots (- 0.88150 \dots)^{6} - 16.54567 \dots (- 0.88150 \dots)^{5} - 14.02314 \dots (- 0.88150 \dots)^{4} - 11.40979 \dots (- 0.88150 \dots)^{3} - 8.70324 \dots (- 0.88150 \dots)^{2} - 1.90109 \dots (- 0.88150 \dots) - 0.96675 \dots = - 3.50205 \dots

u_{3} = - 0.81453 \dots

Δ u_{3} = ∣ - 0.81453 \dots - (- 0.88150 \dots) ∣ = 0.06696 \dots

Δ u_{3} = 0.06696 \dots

u_{4} = - 0.79319 \dots : Δ u_{4} = 0.02134 \dots

f (u_{3}) = - 2 (- 0.81453 \dots)^{25} - 2.03409 \dots (- 0.81453 \dots)^{24} - 2.06878 \dots (- 0.81453 \dots)^{23} - 2.10405 \dots (- 0.81453 \dots)^{22} - 2.13992 \dots (- 0.81453 \dots)^{21} - 2.17641 \dots (- 0.81453 \dots)^{20} - 2.21352 \dots (- 0.81453 \dots)^{19} - 2.25126 \dots (- 0.81453 \dots)^{18} - 2.28964 \dots (- 0.81453 \dots)^{17} - 2.32868 \dots (- 0.81453 \dots)^{16} - 2.36838 \dots (- 0.81453 \dots)^{15} - 2.40876 \dots (- 0.81453 \dots)^{14} - 2.44983 \dots (- 0.81453 \dots)^{13} - 2.49160 \dots (- 0.81453 \dots)^{12} - 2.53408 \dots (- 0.81453 \dots)^{11} - 2.57729 \dots (- 0.81453 \dots)^{10} - 2.62123 \dots (- 0.81453 \dots)^{9} - 2.66592 \dots (- 0.81453 \dots)^{8} - 2.71138 \dots (- 0.81453 \dots)^{7} - 2.75761 \dots (- 0.81453 \dots)^{6} - 2.80462 \dots (- 0.81453 \dots)^{5} - 2.85244 \dots (- 0.81453 \dots)^{4} - 2.90108 \dots (- 0.81453 \dots)^{3} - 0.95054 \dots (- 0.81453 \dots)^{2} - 0.96675 \dots (- 0.81453 \dots) - 0.98323 \dots = 0.04940 \dots

f^{^{'}} (u_{3}) = - 50 (- 0.81453 \dots)^{24} - 48.81839 \dots (- 0.81453 \dots)^{23} - 47.58196 \dots (- 0.81453 \dots)^{22} - 46.28918 \dots (- 0.81453 \dots)^{21} - 44.93848 \dots (- 0.81453 \dots)^{20} - 43.52826 \dots (- 0.81453 \dots)^{19} - 42.05690 \dots (- 0.81453 \dots)^{18} - 40.52270 \dots (- 0.81453 \dots)^{17} - 38.92397 \dots (- 0.81453 \dots)^{16} - 37.25893 \dots (- 0.81453 \dots)^{15} - 35.52581 \dots (- 0.81453 \dots)^{14} - 33.72275 \dots (- 0.81453 \dots)^{13} - 31.84789 \dots (- 0.81453 \dots)^{12} - 29.89928 \dots (- 0.81453 \dots)^{11} - 27.87498 \dots (- 0.81453 \dots)^{10} - 25.77295 \dots (- 0.81453 \dots)^{9} - 23.59114 \dots (- 0.81453 \dots)^{8} - 21.32743 \dots (- 0.81453 \dots)^{7} - 18.97968 \dots (- 0.81453 \dots)^{6} - 16.54567 \dots (- 0.81453 \dots)^{5} - 14.02314 \dots (- 0.81453 \dots)^{4} - 11.40979 \dots (- 0.81453 \dots)^{3} - 8.70324 \dots (- 0.81453 \dots)^{2} - 1.90109 \dots (- 0.81453 \dots) - 0.96675 \dots = - 2.31469 \dots

u_{4} = - 0.79319 \dots

Δ u_{4} = ∣ - 0.79319 \dots - (- 0.81453 \dots) ∣ = 0.02134 \dots

Δ u_{4} = 0.02134 \dots

u_{5} = - 0.79244 \dots : Δ u_{5} = 0.00074 \dots

f (u_{4}) = - 2 (- 0.79319 \dots)^{25} - 2.03409 \dots (- 0.79319 \dots)^{24} - 2.06878 \dots (- 0.79319 \dots)^{23} - 2.10405 \dots (- 0.79319 \dots)^{22} - 2.13992 \dots (- 0.79319 \dots)^{21} - 2.17641 \dots (- 0.79319 \dots)^{20} - 2.21352 \dots (- 0.79319 \dots)^{19} - 2.25126 \dots (- 0.79319 \dots)^{18} - 2.28964 \dots (- 0.79319 \dots)^{17} - 2.32868 \dots (- 0.79319 \dots)^{16} - 2.36838 \dots (- 0.79319 \dots)^{15} - 2.40876 \dots (- 0.79319 \dots)^{14} - 2.44983 \dots (- 0.79319 \dots)^{13} - 2.49160 \dots (- 0.79319 \dots)^{12} - 2.53408 \dots (- 0.79319 \dots)^{11} - 2.57729 \dots (- 0.79319 \dots)^{10} - 2.62123 \dots (- 0.79319 \dots)^{9} - 2.66592 \dots (- 0.79319 \dots)^{8} - 2.71138 \dots (- 0.79319 \dots)^{7} - 2.75761 \dots (- 0.79319 \dots)^{6} - 2.80462 \dots (- 0.79319 \dots)^{5} - 2.85244 \dots (- 0.79319 \dots)^{4} - 2.90108 \dots (- 0.79319 \dots)^{3} - 0.95054 \dots (- 0.79319 \dots)^{2} - 0.96675 \dots (- 0.79319 \dots) - 0.98323 \dots = 0.00161 \dots

f^{^{'}} (u_{4}) = - 50 (- 0.79319 \dots)^{24} - 48.81839 \dots (- 0.79319 \dots)^{23} - 47.58196 \dots (- 0.79319 \dots)^{22} - 46.28918 \dots (- 0.79319 \dots)^{21} - 44.93848 \dots (- 0.79319 \dots)^{20} - 43.52826 \dots (- 0.79319 \dots)^{19} - 42.05690 \dots (- 0.79319 \dots)^{18} - 40.52270 \dots (- 0.79319 \dots)^{17} - 38.92397 \dots (- 0.79319 \dots)^{16} - 37.25893 \dots (- 0.79319 \dots)^{15} - 35.52581 \dots (- 0.79319 \dots)^{14} - 33.72275 \dots (- 0.79319 \dots)^{13} - 31.84789 \dots (- 0.79319 \dots)^{12} - 29.89928 \dots (- 0.79319 \dots)^{11} - 27.87498 \dots (- 0.79319 \dots)^{10} - 25.77295 \dots (- 0.79319 \dots)^{9} - 23.59114 \dots (- 0.79319 \dots)^{8} - 21.32743 \dots (- 0.79319 \dots)^{7} - 18.97968 \dots (- 0.79319 \dots)^{6} - 16.54567 \dots (- 0.79319 \dots)^{5} - 14.02314 \dots (- 0.79319 \dots)^{4} - 11.40979 \dots (- 0.79319 \dots)^{3} - 8.70324 \dots (- 0.79319 \dots)^{2} - 1.90109 \dots (- 0.79319 \dots) - 0.96675 \dots = - 2.17206 \dots

u_{5} = - 0.79244 \dots

Δ u_{5} = ∣ - 0.79244 \dots - (- 0.79319 \dots) ∣ = 0.00074 \dots

Δ u_{5} = 0.00074 \dots

u_{6} = - 0.79244 \dots : Δ u_{6} = 7.10666 E - 7

f (u_{5}) = - 2 (- 0.79244 \dots)^{25} - 2.03409 \dots (- 0.79244 \dots)^{24} - 2.06878 \dots (- 0.79244 \dots)^{23} - 2.10405 \dots (- 0.79244 \dots)^{22} - 2.13992 \dots (- 0.79244 \dots)^{21} - 2.17641 \dots (- 0.79244 \dots)^{20} - 2.21352 \dots (- 0.79244 \dots)^{19} - 2.25126 \dots (- 0.79244 \dots)^{18} - 2.28964 \dots (- 0.79244 \dots)^{17} - 2.32868 \dots (- 0.79244 \dots)^{16} - 2.36838 \dots (- 0.79244 \dots)^{15} - 2.40876 \dots (- 0.79244 \dots)^{14} - 2.44983 \dots (- 0.79244 \dots)^{13} - 2.49160 \dots (- 0.79244 \dots)^{12} - 2.53408 \dots (- 0.79244 \dots)^{11} - 2.57729 \dots (- 0.79244 \dots)^{10} - 2.62123 \dots (- 0.79244 \dots)^{9} - 2.66592 \dots (- 0.79244 \dots)^{8} - 2.71138 \dots (- 0.79244 \dots)^{7} - 2.75761 \dots (- 0.79244 \dots)^{6} - 2.80462 \dots (- 0.79244 \dots)^{5} - 2.85244 \dots (- 0.79244 \dots)^{4} - 2.90108 \dots (- 0.79244 \dots)^{3} - 0.95054 \dots (- 0.79244 \dots)^{2} - 0.96675 \dots (- 0.79244 \dots) - 0.98323 \dots = 1.54066 E - 6

f^{^{'}} (u_{5}) = - 50 (- 0.79244 \dots)^{24} - 48.81839 \dots (- 0.79244 \dots)^{23} - 47.58196 \dots (- 0.79244 \dots)^{22} - 46.28918 \dots (- 0.79244 \dots)^{21} - 44.93848 \dots (- 0.79244 \dots)^{20} - 43.52826 \dots (- 0.79244 \dots)^{19} - 42.05690 \dots (- 0.79244 \dots)^{18} - 40.52270 \dots (- 0.79244 \dots)^{17} - 38.92397 \dots (- 0.79244 \dots)^{16} - 37.25893 \dots (- 0.79244 \dots)^{15} - 35.52581 \dots (- 0.79244 \dots)^{14} - 33.72275 \dots (- 0.79244 \dots)^{13} - 31.84789 \dots (- 0.79244 \dots)^{12} - 29.89928 \dots (- 0.79244 \dots)^{11} - 27.87498 \dots (- 0.79244 \dots)^{10} - 25.77295 \dots (- 0.79244 \dots)^{9} - 23.59114 \dots (- 0.79244 \dots)^{8} - 21.32743 \dots (- 0.79244 \dots)^{7} - 18.97968 \dots (- 0.79244 \dots)^{6} - 16.54567 \dots (- 0.79244 \dots)^{5} - 14.02314 \dots (- 0.79244 \dots)^{4} - 11.40979 \dots (- 0.79244 \dots)^{3} - 8.70324 \dots (- 0.79244 \dots)^{2} - 1.90109 \dots (- 0.79244 \dots) - 0.96675 \dots = - 2.16791 \dots

u_{6} = - 0.79244 \dots

Δ u_{6} = ∣ - 0.79244 \dots - (- 0.79244 \dots) ∣ = 7.10666 E - 7

Δ u_{6} = 7.10666 E - 7

u \approx - 0.79244 \dots

Apply long division:

\frac{- 2 u ^{25} - 2.03409 \dots u ^{24} - 2.06878 \dots u ^{23} - 2.10405 \dots u ^{22} - 2.13992 \dots u ^{21} - 2.17641 \dots u ^{20} - 2.21352 \dots u ^{19} - 2.25126 \dots u ^{18} - 2.28964 \dots u ^{17} - 2.32868 \dots u ^{16} - 2.36838 \dots u ^{15} - 2.40876 \dots u ^{14} - 2.44983 \dots u ^{13} - 2.49160 \dots u ^{12} - 2.53408 \dots u ^{11} - 2.57729 \dots u ^{10} - 2.62123 \dots u ^{9} - 2.66592 \dots u ^{8} - 2.71138 \dots u ^{7} - 2.75761 \dots u ^{6} - 2.80462 \dots u ^{5} - 2.85244 \dots u ^{4} - 2.90108 \dots u ^{3} - 0.95054 \dots u ^{2} - 0.96675 \dots u - 0.98323 \dots}{u + 0.79244 \dots} = - 2 u^{24} - 0.44920 \dots u^{23} - 1.71281 \dots u^{22} - 0.74673 \dots u^{21} - 1.54817 \dots u^{20} - 0.94956 \dots u^{19} - 1.46104 \dots u^{18} - 1.09346 \dots u^{17} - 1.42313 \dots u^{16} - 1.20092 \dots u^{15} - 1.41671 \dots u^{14} - 1.28609 \dots u^{13} - 1.43067 \dots u^{12} - 1.35787 \dots u^{11} - 1.45804 \dots u^{10} - 1.42186 \dots u^{9} - 1.49448 \dots u^{8} - 1.48163 \dots u^{7} - 1.53726 \dots u^{6} - 1.53940 \dots u^{5} - 1.58472 \dots u^{4} - 1.59663 \dots u^{3} - 1.63583 \dots u^{2} + 0.34576 \dots u - 1.24075 \dots

- 2 u^{24} - 0.44920 \dots u^{23} - 1.71281 \dots u^{22} - 0.74673 \dots u^{21} - 1.54817 \dots u^{20} - 0.94956 \dots u^{19} - 1.46104 \dots u^{18} - 1.09346 \dots u^{17} - 1.42313 \dots u^{16} - 1.20092 \dots u^{15} - 1.41671 \dots u^{14} - 1.28609 \dots u^{13} - 1.43067 \dots u^{12} - 1.35787 \dots u^{11} - 1.45804 \dots u^{10} - 1.42186 \dots u^{9} - 1.49448 \dots u^{8} - 1.48163 \dots u^{7} - 1.53726 \dots u^{6} - 1.53940 \dots u^{5} - 1.58472 \dots u^{4} - 1.59663 \dots u^{3} - 1.63583 \dots u^{2} + 0.34576 \dots u - 1.24075 \dots \approx 0

Find one solution for

- 2 u^{24} - 0.44920 \dots u^{23} - 1.71281 \dots u^{22} - 0.74673 \dots u^{21} - 1.54817 \dots u^{20} - 0.94956 \dots u^{19} - 1.46104 \dots u^{18} - 1.09346 \dots u^{17} - 1.42313 \dots u^{16} - 1.20092 \dots u^{15} - 1.41671 \dots u^{14} - 1.28609 \dots u^{13} - 1.43067 \dots u^{12} - 1.35787 \dots u^{11} - 1.45804 \dots u^{10} - 1.42186 \dots u^{9} - 1.49448 \dots u^{8} - 1.48163 \dots u^{7} - 1.53726 \dots u^{6} - 1.53940 \dots u^{5} - 1.58472 \dots u^{4} - 1.59663 \dots u^{3} - 1.63583 \dots u^{2} + 0.34576 \dots u - 1.24075 \dots = 0

using Newton-Raphson:

No Solution for

u \in R

- 2 u^{24} - 0.44920 \dots u^{23} - 1.71281 \dots u^{22} - 0.74673 \dots u^{21} - 1.54817 \dots u^{20} - 0.94956 \dots u^{19} - 1.46104 \dots u^{18} - 1.09346 \dots u^{17} - 1.42313 \dots u^{16} - 1.20092 \dots u^{15} - 1.41671 \dots u^{14} - 1.28609 \dots u^{13} - 1.43067 \dots u^{12} - 1.35787 \dots u^{11} - 1.45804 \dots u^{10} - 1.42186 \dots u^{9} - 1.49448 \dots u^{8} - 1.48163 \dots u^{7} - 1.53726 \dots u^{6} - 1.53940 \dots u^{5} - 1.58472 \dots u^{4} - 1.59663 \dots u^{3} - 1.63583 \dots u^{2} + 0.34576 \dots u - 1.24075 \dots = 0

Newton-Raphson Approximation Definition

f (u) = - 2 u^{24} - 0.44920 \dots u^{23} - 1.71281 \dots u^{22} - 0.74673 \dots u^{21} - 1.54817 \dots u^{20} - 0.94956 \dots u^{19} - 1.46104 \dots u^{18} - 1.09346 \dots u^{17} - 1.42313 \dots u^{16} - 1.20092 \dots u^{15} - 1.41671 \dots u^{14} - 1.28609 \dots u^{13} - 1.43067 \dots u^{12} - 1.35787 \dots u^{11} - 1.45804 \dots u^{10} - 1.42186 \dots u^{9} - 1.49448 \dots u^{8} - 1.48163 \dots u^{7} - 1.53726 \dots u^{6} - 1.53940 \dots u^{5} - 1.58472 \dots u^{4} - 1.59663 \dots u^{3} - 1.63583 \dots u^{2} + 0.34576 \dots u - 1.24075 \dots

Find

f^{^{'}} (u) : - 48 u^{23} - 10.33165 \dots u^{22} - 37.68185 \dots u^{21} - 15.68150 \dots u^{20} - 30.96351 \dots u^{19} - 18.04170 \dots u^{18} - 26.29873 \dots u^{17} - 18.58884 \dots u^{16} - 22.77013 \dots u^{15} - 18.01385 \dots u^{14} - 19.83404 \dots u^{13} - 16.71920 \dots u^{12} - 17.16810 \dots u^{11} - 14.93657 \dots u^{10} - 14.58046 \dots u^{9} - 12.79681 \dots u^{8} - 11.95584 \dots u^{7} - 10.37141 \dots u^{6} - 9.22360 \dots u^{5} - 7.69703 \dots u^{4} - 6.33891 \dots u^{3} - 4.78989 \dots u^{2} - 3.27166 \dots u + 0.34576 \dots

Let

u_{0} = 4

Compute

u_{n + 1}

until

Δ u_{n + 1} < 0.000001

u_{1} = 3.83210 \dots : Δ u_{1} = 0.16789 \dots

f (u_{0}) = - 2 \cdot 4^{24} - 0.44920 \dots \cdot 4^{23} - 1.71281 \dots \cdot 4^{22} - 0.74673 \dots \cdot 4^{21} - 1.54817 \dots \cdot 4^{20} - 0.94956 \dots \cdot 4^{19} - 1.46104 \dots \cdot 4^{18} - 1.09346 \dots \cdot 4^{17} - 1.42313 \dots \cdot 4^{16} - 1.20092 \dots \cdot 4^{15} - 1.41671 \dots \cdot 4^{14} - 1.28609 \dots \cdot 4^{13} - 1.43067 \dots \cdot 4^{12} - 1.35787 \dots \cdot 4^{11} - 1.45804 \dots \cdot 4^{10} - 1.42186 \dots \cdot 4^{9} - 1.49448 \dots \cdot 4^{8} - 1.48163 \dots \cdot 4^{7} - 1.53726 \dots \cdot 4^{6} - 1.53940 \dots \cdot 4^{5} - 1.58472 \dots \cdot 4^{4} - 1.59663 \dots \cdot 4^{3} - 1.63583 \dots \cdot 4^{2} + 0.34576 \dots \cdot 4 - 1.24075 \dots = - 6.30066 E 14

f^{^{'}} (u_{0}) = - 48 \cdot 4^{23} - 10.33165 \dots \cdot 4^{22} - 37.68185 \dots \cdot 4^{21} - 15.68150 \dots \cdot 4^{20} - 30.96351 \dots \cdot 4^{19} - 18.04170 \dots \cdot 4^{18} - 26.29873 \dots \cdot 4^{17} - 18.58884 \dots \cdot 4^{16} - 22.77013 \dots \cdot 4^{15} - 18.01385 \dots \cdot 4^{14} - 19.83404 \dots \cdot 4^{13} - 16.71920 \dots \cdot 4^{12} - 17.16810 \dots \cdot 4^{11} - 14.93657 \dots \cdot 4^{10} - 14.58046 \dots \cdot 4^{9} - 12.79681 \dots \cdot 4^{8} - 11.95584 \dots \cdot 4^{7} - 10.37141 \dots \cdot 4^{6} - 9.22360 \dots \cdot 4^{5} - 7.69703 \dots \cdot 4^{4} - 6.33891 \dots \cdot 4^{3} - 4.78989 \dots \cdot 4^{2} - 3.27166 \dots \cdot 4 + 0.34576 \dots = - 3.75274 E 15

u_{1} = 3.83210 \dots

Δ u_{1} = ∣ 3.83210 \dots - 4 ∣ = 0.16789 \dots

Δ u_{1} = 0.16789 \dots

u_{2} = 3.67116 \dots : Δ u_{2} = 0.16094 \dots

f (u_{1}) = - 2 \cdot 3.83210 \dots^{24} - 0.44920 \dots \cdot 3.83210 \dots^{23} - 1.71281 \dots \cdot 3.83210 \dots^{22} - 0.74673 \dots \cdot 3.83210 \dots^{21} - 1.54817 \dots \cdot 3.83210 \dots^{20} - 0.94956 \dots \cdot 3.83210 \dots^{19} - 1.46104 \dots \cdot 3.83210 \dots^{18} - 1.09346 \dots \cdot 3.83210 \dots^{17} - 1.42313 \dots \cdot 3.83210 \dots^{16} - 1.20092 \dots \cdot 3.83210 \dots^{15} - 1.41671 \dots \cdot 3.83210 \dots^{14} - 1.28609 \dots \cdot 3.83210 \dots^{13} - 1.43067 \dots \cdot 3.83210 \dots^{12} - 1.35787 \dots \cdot 3.83210 \dots^{11} - 1.45804 \dots \cdot 3.83210 \dots^{10} - 1.42186 \dots \cdot 3.83210 \dots^{9} - 1.49448 \dots \cdot 3.83210 \dots^{8} - 1.48163 \dots \cdot 3.83210 \dots^{7} - 1.53726 \dots \cdot 3.83210 \dots^{6} - 1.53940 \dots \cdot 3.83210 \dots^{5} - 1.58472 \dots \cdot 3.83210 \dots^{4} - 1.59663 \dots \cdot 3.83210 \dots^{3} - 1.63583 \dots \cdot 3.83210 \dots^{2} + 0.34576 \dots \cdot 3.83210 \dots - 1.24075 \dots = - 2.26906 E 14

f^{^{'}} (u_{1}) = - 48 \cdot 3.83210 \dots^{23} - 10.33165 \dots \cdot 3.83210 \dots^{22} - 37.68185 \dots \cdot 3.83210 \dots^{21} - 15.68150 \dots \cdot 3.83210 \dots^{20} - 30.96351 \dots \cdot 3.83210 \dots^{19} - 18.04170 \dots \cdot 3.83210 \dots^{18} - 26.29873 \dots \cdot 3.83210 \dots^{17} - 18.58884 \dots \cdot 3.83210 \dots^{16} - 22.77013 \dots \cdot 3.83210 \dots^{15} - 18.01385 \dots \cdot 3.83210 \dots^{14} - 19.83404 \dots \cdot 3.83210 \dots^{13} - 16.71920 \dots \cdot 3.83210 \dots^{12} - 17.16810 \dots \cdot 3.83210 \dots^{11} - 14.93657 \dots \cdot 3.83210 \dots^{10} - 14.58046 \dots \cdot 3.83210 \dots^{9} - 12.79681 \dots \cdot 3.83210 \dots^{8} - 11.95584 \dots \cdot 3.83210 \dots^{7} - 10.37141 \dots \cdot 3.83210 \dots^{6} - 9.22360 \dots \cdot 3.83210 \dots^{5} - 7.69703 \dots \cdot 3.83210 \dots^{4} - 6.33891 \dots \cdot 3.83210 \dots^{3} - 4.78989 \dots \cdot 3.83210 \dots^{2} - 3.27166 \dots \cdot 3.83210 \dots + 0.34576 \dots = - 1.40984 E 15

u_{2} = 3.67116 \dots

Δ u_{2} = ∣ 3.67116 \dots - 3.83210 \dots ∣ = 0.16094 \dots

Δ u_{2} = 0.16094 \dots

u_{3} = 3.51687 \dots : Δ u_{3} = 0.15428 \dots

f (u_{2}) = - 2 \cdot 3.67116 \dots^{24} - 0.44920 \dots \cdot 3.67116 \dots^{23} - 1.71281 \dots \cdot 3.67116 \dots^{22} - 0.74673 \dots \cdot 3.67116 \dots^{21} - 1.54817 \dots \cdot 3.67116 \dots^{20} - 0.94956 \dots \cdot 3.67116 \dots^{19} - 1.46104 \dots \cdot 3.67116 \dots^{18} - 1.09346 \dots \cdot 3.67116 \dots^{17} - 1.42313 \dots \cdot 3.67116 \dots^{16} - 1.20092 \dots \cdot 3.67116 \dots^{15} - 1.41671 \dots \cdot 3.67116 \dots^{14} - 1.28609 \dots \cdot 3.67116 \dots^{13} - 1.43067 \dots \cdot 3.67116 \dots^{12} - 1.35787 \dots \cdot 3.67116 \dots^{11} - 1.45804 \dots \cdot 3.67116 \dots^{10} - 1.42186 \dots \cdot 3.67116 \dots^{9} - 1.49448 \dots \cdot 3.67116 \dots^{8} - 1.48163 \dots \cdot 3.67116 \dots^{7} - 1.53726 \dots \cdot 3.67116 \dots^{6} - 1.53940 \dots \cdot 3.67116 \dots^{5} - 1.58472 \dots \cdot 3.67116 \dots^{4} - 1.59663 \dots \cdot 3.67116 \dots^{3} - 1.63583 \dots \cdot 3.67116 \dots^{2} + 0.34576 \dots \cdot 3.67116 \dots - 1.24075 \dots = - 8.17168 E 13

f^{^{'}} (u_{2}) = - 48 \cdot 3.67116 \dots^{23} - 10.33165 \dots \cdot 3.67116 \dots^{22} - 37.68185 \dots \cdot 3.67116 \dots^{21} - 15.68150 \dots \cdot 3.67116 \dots^{20} - 30.96351 \dots \cdot 3.67116 \dots^{19} - 18.04170 \dots \cdot 3.67116 \dots^{18} - 26.29873 \dots \cdot 3.67116 \dots^{17} - 18.58884 \dots \cdot 3.67116 \dots^{16} - 22.77013 \dots \cdot 3.67116 \dots^{15} - 18.01385 \dots \cdot 3.67116 \dots^{14} - 19.83404 \dots \cdot 3.67116 \dots^{13} - 16.71920 \dots \cdot 3.67116 \dots^{12} - 17.16810 \dots \cdot 3.67116 \dots^{11} - 14.93657 \dots \cdot 3.67116 \dots^{10} - 14.58046 \dots \cdot 3.67116 \dots^{9} - 12.79681 \dots \cdot 3.67116 \dots^{8} - 11.95584 \dots \cdot 3.67116 \dots^{7} - 10.37141 \dots \cdot 3.67116 \dots^{6} - 9.22360 \dots \cdot 3.67116 \dots^{5} - 7.69703 \dots \cdot 3.67116 \dots^{4} - 6.33891 \dots \cdot 3.67116 \dots^{3} - 4.78989 \dots \cdot 3.67116 \dots^{2} - 3.27166 \dots \cdot 3.67116 \dots + 0.34576 \dots = - 5.29641 E 14

u_{3} = 3.51687 \dots

Δ u_{3} = ∣ 3.51687 \dots - 3.67116 \dots ∣ = 0.15428 \dots

Δ u_{3} = 0.15428 \dots

u_{4} = 3.36896 \dots : Δ u_{4} = 0.14791 \dots

f (u_{3}) = - 2 \cdot 3.51687 \dots^{24} - 0.44920 \dots \cdot 3.51687 \dots^{23} - 1.71281 \dots \cdot 3.51687 \dots^{22} - 0.74673 \dots \cdot 3.51687 \dots^{21} - 1.54817 \dots \cdot 3.51687 \dots^{20} - 0.94956 \dots \cdot 3.51687 \dots^{19} - 1.46104 \dots \cdot 3.51687 \dots^{18} - 1.09346 \dots \cdot 3.51687 \dots^{17} - 1.42313 \dots \cdot 3.51687 \dots^{16} - 1.20092 \dots \cdot 3.51687 \dots^{15} - 1.41671 \dots \cdot 3.51687 \dots^{14} - 1.28609 \dots \cdot 3.51687 \dots^{13} - 1.43067 \dots \cdot 3.51687 \dots^{12} - 1.35787 \dots \cdot 3.51687 \dots^{11} - 1.45804 \dots \cdot 3.51687 \dots^{10} - 1.42186 \dots \cdot 3.51687 \dots^{9} - 1.49448 \dots \cdot 3.51687 \dots^{8} - 1.48163 \dots \cdot 3.51687 \dots^{7} - 1.53726 \dots \cdot 3.51687 \dots^{6} - 1.53940 \dots \cdot 3.51687 \dots^{5} - 1.58472 \dots \cdot 3.51687 \dots^{4} - 1.59663 \dots \cdot 3.51687 \dots^{3} - 1.63583 \dots \cdot 3.51687 \dots^{2} + 0.34576 \dots \cdot 3.51687 \dots - 1.24075 \dots = - 2.94297 E 13

f^{^{'}} (u_{3}) = - 48 \cdot 3.51687 \dots^{23} - 10.33165 \dots \cdot 3.51687 \dots^{22} - 37.68185 \dots \cdot 3.51687 \dots^{21} - 15.68150 \dots \cdot 3.51687 \dots^{20} - 30.96351 \dots \cdot 3.51687 \dots^{19} - 18.04170 \dots \cdot 3.51687 \dots^{18} - 26.29873 \dots \cdot 3.51687 \dots^{17} - 18.58884 \dots \cdot 3.51687 \dots^{16} - 22.77013 \dots \cdot 3.51687 \dots^{15} - 18.01385 \dots \cdot 3.51687 \dots^{14} - 19.83404 \dots \cdot 3.51687 \dots^{13} - 16.71920 \dots \cdot 3.51687 \dots^{12} - 17.16810 \dots \cdot 3.51687 \dots^{11} - 14.93657 \dots \cdot 3.51687 \dots^{10} - 14.58046 \dots \cdot 3.51687 \dots^{9} - 12.79681 \dots \cdot 3.51687 \dots^{8} - 11.95584 \dots \cdot 3.51687 \dots^{7} - 10.37141 \dots \cdot 3.51687 \dots^{6} - 9.22360 \dots \cdot 3.51687 \dots^{5} - 7.69703 \dots \cdot 3.51687 \dots^{4} - 6.33891 \dots \cdot 3.51687 \dots^{3} - 4.78989 \dots \cdot 3.51687 \dots^{2} - 3.27166 \dots \cdot 3.51687 \dots + 0.34576 \dots = - 1.9897 E 14

u_{4} = 3.36896 \dots

Δ u_{4} = ∣ 3.36896 \dots - 3.51687 \dots ∣ = 0.14791 \dots

Δ u_{4} = 0.14791 \dots

u_{5} = 3.22715 \dots : Δ u_{5} = 0.14180 \dots

f (u_{4}) = - 2 \cdot 3.36896 \dots^{24} - 0.44920 \dots \cdot 3.36896 \dots^{23} - 1.71281 \dots \cdot 3.36896 \dots^{22} - 0.74673 \dots \cdot 3.36896 \dots^{21} - 1.54817 \dots \cdot 3.36896 \dots^{20} - 0.94956 \dots \cdot 3.36896 \dots^{19} - 1.46104 \dots \cdot 3.36896 \dots^{18} - 1.09346 \dots \cdot 3.36896 \dots^{17} - 1.42313 \dots \cdot 3.36896 \dots^{16} - 1.20092 \dots \cdot 3.36896 \dots^{15} - 1.41671 \dots \cdot 3.36896 \dots^{14} - 1.28609 \dots \cdot 3.36896 \dots^{13} - 1.43067 \dots \cdot 3.36896 \dots^{12} - 1.35787 \dots \cdot 3.36896 \dots^{11} - 1.45804 \dots \cdot 3.36896 \dots^{10} - 1.42186 \dots \cdot 3.36896 \dots^{9} - 1.49448 \dots \cdot 3.36896 \dots^{8} - 1.48163 \dots \cdot 3.36896 \dots^{7} - 1.53726 \dots \cdot 3.36896 \dots^{6} - 1.53940 \dots \cdot 3.36896 \dots^{5} - 1.58472 \dots \cdot 3.36896 \dots^{4} - 1.59663 \dots \cdot 3.36896 \dots^{3} - 1.63583 \dots \cdot 3.36896 \dots^{2} + 0.34576 \dots \cdot 3.36896 \dots - 1.24075 \dots = - 1.05991 E 13

f^{^{'}} (u_{4}) = - 48 \cdot 3.36896 \dots^{23} - 10.33165 \dots \cdot 3.36896 \dots^{22} - 37.68185 \dots \cdot 3.36896 \dots^{21} - 15.68150 \dots \cdot 3.36896 \dots^{20} - 30.96351 \dots \cdot 3.36896 \dots^{19} - 18.04170 \dots \cdot 3.36896 \dots^{18} - 26.29873 \dots \cdot 3.36896 \dots^{17} - 18.58884 \dots \cdot 3.36896 \dots^{16} - 22.77013 \dots \cdot 3.36896 \dots^{15} - 18.01385 \dots \cdot 3.36896 \dots^{14} - 19.83404 \dots \cdot 3.36896 \dots^{13} - 16.71920 \dots \cdot 3.36896 \dots^{12} - 17.16810 \dots \cdot 3.36896 \dots^{11} - 14.93657 \dots \cdot 3.36896 \dots^{10} - 14.58046 \dots \cdot 3.36896 \dots^{9} - 12.79681 \dots \cdot 3.36896 \dots^{8} - 11.95584 \dots \cdot 3.36896 \dots^{7} - 10.37141 \dots \cdot 3.36896 \dots^{6} - 9.22360 \dots \cdot 3.36896 \dots^{5} - 7.69703 \dots \cdot 3.36896 \dots^{4} - 6.33891 \dots \cdot 3.36896 \dots^{3} - 4.78989 \dots \cdot 3.36896 \dots^{2} - 3.27166 \dots \cdot 3.36896 \dots + 0.34576 \dots = - 7.47451 E 13

u_{5} = 3.22715 \dots

Δ u_{5} = ∣ 3.22715 \dots - 3.36896 \dots ∣ = 0.14180 \dots

Δ u_{5} = 0.14180 \dots

u_{6} = 3.09120 \dots : Δ u_{6} = 0.13595 \dots

f (u_{5}) = - 2 \cdot 3.22715 \dots^{24} - 0.44920 \dots \cdot 3.22715 \dots^{23} - 1.71281 \dots \cdot 3.22715 \dots^{22} - 0.74673 \dots \cdot 3.22715 \dots^{21} - 1.54817 \dots \cdot 3.22715 \dots^{20} - 0.94956 \dots \cdot 3.22715 \dots^{19} - 1.46104 \dots \cdot 3.22715 \dots^{18} - 1.09346 \dots \cdot 3.22715 \dots^{17} - 1.42313 \dots \cdot 3.22715 \dots^{16} - 1.20092 \dots \cdot 3.22715 \dots^{15} - 1.41671 \dots \cdot 3.22715 \dots^{14} - 1.28609 \dots \cdot 3.22715 \dots^{13} - 1.43067 \dots \cdot 3.22715 \dots^{12} - 1.35787 \dots \cdot 3.22715 \dots^{11} - 1.45804 \dots \cdot 3.22715 \dots^{10} - 1.42186 \dots \cdot 3.22715 \dots^{9} - 1.49448 \dots \cdot 3.22715 \dots^{8} - 1.48163 \dots \cdot 3.22715 \dots^{7} - 1.53726 \dots \cdot 3.22715 \dots^{6} - 1.53940 \dots \cdot 3.22715 \dots^{5} - 1.58472 \dots \cdot 3.22715 \dots^{4} - 1.59663 \dots \cdot 3.22715 \dots^{3} - 1.63583 \dots \cdot 3.22715 \dots^{2} + 0.34576 \dots \cdot 3.22715 \dots - 1.24075 \dots = - 3817357592971.301

f^{^{'}} (u_{5}) = - 48 \cdot 3.22715 \dots^{23} - 10.33165 \dots \cdot 3.22715 \dots^{22} - 37.68185 \dots \cdot 3.22715 \dots^{21} - 15.68150 \dots \cdot 3.22715 \dots^{20} - 30.96351 \dots \cdot 3.22715 \dots^{19} - 18.04170 \dots \cdot 3.22715 \dots^{18} - 26.29873 \dots \cdot 3.22715 \dots^{17} - 18.58884 \dots \cdot 3.22715 \dots^{16} - 22.77013 \dots \cdot 3.22715 \dots^{15} - 18.01385 \dots \cdot 3.22715 \dots^{14} - 19.83404 \dots \cdot 3.22715 \dots^{13} - 16.71920 \dots \cdot 3.22715 \dots^{12} - 17.16810 \dots \cdot 3.22715 \dots^{11} - 14.93657 \dots \cdot 3.22715 \dots^{10} - 14.58046 \dots \cdot 3.22715 \dots^{9} - 12.79681 \dots \cdot 3.22715 \dots^{8} - 11.95584 \dots \cdot 3.22715 \dots^{7} - 10.37141 \dots \cdot 3.22715 \dots^{6} - 9.22360 \dots \cdot 3.22715 \dots^{5} - 7.69703 \dots \cdot 3.22715 \dots^{4} - 6.33891 \dots \cdot 3.22715 \dots^{3} - 4.78989 \dots \cdot 3.22715 \dots^{2} - 3.27166 \dots \cdot 3.22715 \dots + 0.34576 \dots = - 2.80781 E 13

u_{6} = 3.09120 \dots

Δ u_{6} = ∣ 3.09120 \dots - 3.22715 \dots ∣ = 0.13595 \dots

Δ u_{6} = 0.13595 \dots

u_{7} = 2.96084 \dots : Δ u_{7} = 0.13035 \dots

f (u_{6}) = - 2 \cdot 3.09120 \dots^{24} - 0.44920 \dots \cdot 3.09120 \dots^{23} - 1.71281 \dots \cdot 3.09120 \dots^{22} - 0.74673 \dots \cdot 3.09120 \dots^{21} - 1.54817 \dots \cdot 3.09120 \dots^{20} - 0.94956 \dots \cdot 3.09120 \dots^{19} - 1.46104 \dots \cdot 3.09120 \dots^{18} - 1.09346 \dots \cdot 3.09120 \dots^{17} - 1.42313 \dots \cdot 3.09120 \dots^{16} - 1.20092 \dots \cdot 3.09120 \dots^{15} - 1.41671 \dots \cdot 3.09120 \dots^{14} - 1.28609 \dots \cdot 3.09120 \dots^{13} - 1.43067 \dots \cdot 3.09120 \dots^{12} - 1.35787 \dots \cdot 3.09120 \dots^{11} - 1.45804 \dots \cdot 3.09120 \dots^{10} - 1.42186 \dots \cdot 3.09120 \dots^{9} - 1.49448 \dots \cdot 3.09120 \dots^{8} - 1.48163 \dots \cdot 3.09120 \dots^{7} - 1.53726 \dots \cdot 3.09120 \dots^{6} - 1.53940 \dots \cdot 3.09120 \dots^{5} - 1.58472 \dots \cdot 3.09120 \dots^{4} - 1.59663 \dots \cdot 3.09120 \dots^{3} - 1.63583 \dots \cdot 3.09120 \dots^{2} + 0.34576 \dots \cdot 3.09120 \dots - 1.24075 \dots = - 1374892424072.9258

f^{^{'}} (u_{6}) = - 48 \cdot 3.09120 \dots^{23} - 10.33165 \dots \cdot 3.09120 \dots^{22} - 37.68185 \dots \cdot 3.09120 \dots^{21} - 15.68150 \dots \cdot 3.09120 \dots^{20} - 30.96351 \dots \cdot 3.09120 \dots^{19} - 18.04170 \dots \cdot 3.09120 \dots^{18} - 26.29873 \dots \cdot 3.09120 \dots^{17} - 18.58884 \dots \cdot 3.09120 \dots^{16} - 22.77013 \dots \cdot 3.09120 \dots^{15} - 18.01385 \dots \cdot 3.09120 \dots^{14} - 19.83404 \dots \cdot 3.09120 \dots^{13} - 16.71920 \dots \cdot 3.09120 \dots^{12} - 17.16810 \dots \cdot 3.09120 \dots^{11} - 14.93657 \dots \cdot 3.09120 \dots^{10} - 14.58046 \dots \cdot 3.09120 \dots^{9} - 12.79681 \dots \cdot 3.09120 \dots^{8} - 11.95584 \dots \cdot 3.09120 \dots^{7} - 10.37141 \dots \cdot 3.09120 \dots^{6} - 9.22360 \dots \cdot 3.09120 \dots^{5} - 7.69703 \dots \cdot 3.09120 \dots^{4} - 6.33891 \dots \cdot 3.09120 \dots^{3} - 4.78989 \dots \cdot 3.09120 \dots^{2} - 3.27166 \dots \cdot 3.09120 \dots + 0.34576 \dots = - 1.05473 E 13

u_{7} = 2.96084 \dots

Δ u_{7} = ∣ 2.96084 \dots - 3.09120 \dots ∣ = 0.13035 \dots

Δ u_{7} = 0.13035 \dots

u_{8} = 2.83585 \dots : Δ u_{8} = 0.12499 \dots

f (u_{7}) = - 2 \cdot 2.96084 \dots^{24} - 0.44920 \dots \cdot 2.96084 \dots^{23} - 1.71281 \dots \cdot 2.96084 \dots^{22} - 0.74673 \dots \cdot 2.96084 \dots^{21} - 1.54817 \dots \cdot 2.96084 \dots^{20} - 0.94956 \dots \cdot 2.96084 \dots^{19} - 1.46104 \dots \cdot 2.96084 \dots^{18} - 1.09346 \dots \cdot 2.96084 \dots^{17} - 1.42313 \dots \cdot 2.96084 \dots^{16} - 1.20092 \dots \cdot 2.96084 \dots^{15} - 1.41671 \dots \cdot 2.96084 \dots^{14} - 1.28609 \dots \cdot 2.96084 \dots^{13} - 1.43067 \dots \cdot 2.96084 \dots^{12} - 1.35787 \dots \cdot 2.96084 \dots^{11} - 1.45804 \dots \cdot 2.96084 \dots^{10} - 1.42186 \dots \cdot 2.96084 \dots^{9} - 1.49448 \dots \cdot 2.96084 \dots^{8} - 1.48163 \dots \cdot 2.96084 \dots^{7} - 1.53726 \dots \cdot 2.96084 \dots^{6} - 1.53940 \dots \cdot 2.96084 \dots^{5} - 1.58472 \dots \cdot 2.96084 \dots^{4} - 1.59663 \dots \cdot 2.96084 \dots^{3} - 1.63583 \dots \cdot 2.96084 \dots^{2} + 0.34576 \dots \cdot 2.96084 \dots - 1.24075 \dots = - 495208989513.3814

f^{^{'}} (u_{7}) = - 48 \cdot 2.96084 \dots^{23} - 10.33165 \dots \cdot 2.96084 \dots^{22} - 37.68185 \dots \cdot 2.96084 \dots^{21} - 15.68150 \dots \cdot 2.96084 \dots^{20} - 30.96351 \dots \cdot 2.96084 \dots^{19} - 18.04170 \dots \cdot 2.96084 \dots^{18} - 26.29873 \dots \cdot 2.96084 \dots^{17} - 18.58884 \dots \cdot 2.96084 \dots^{16} - 22.77013 \dots \cdot 2.96084 \dots^{15} - 18.01385 \dots \cdot 2.96084 \dots^{14} - 19.83404 \dots \cdot 2.96084 \dots^{13} - 16.71920 \dots \cdot 2.96084 \dots^{12} - 17.16810 \dots \cdot 2.96084 \dots^{11} - 14.93657 \dots \cdot 2.96084 \dots^{10} - 14.58046 \dots \cdot 2.96084 \dots^{9} - 12.79681 \dots \cdot 2.96084 \dots^{8} - 11.95584 \dots \cdot 2.96084 \dots^{7} - 10.37141 \dots \cdot 2.96084 \dots^{6} - 9.22360 \dots \cdot 2.96084 \dots^{5} - 7.69703 \dots \cdot 2.96084 \dots^{4} - 6.33891 \dots \cdot 2.96084 \dots^{3} - 4.78989 \dots \cdot 2.96084 \dots^{2} - 3.27166 \dots \cdot 2.96084 \dots + 0.34576 \dots = - 3961858185234.1772

u_{8} = 2.83585 \dots

Δ u_{8} = ∣ 2.83585 \dots - 2.96084 \dots ∣ = 0.12499 \dots

Δ u_{8} = 0.12499 \dots

u_{9} = 2.71599 \dots : Δ u_{9} = 0.11986 \dots

f (u_{8}) = - 2 \cdot 2.83585 \dots^{24} - 0.44920 \dots \cdot 2.83585 \dots^{23} - 1.71281 \dots \cdot 2.83585 \dots^{22} - 0.74673 \dots \cdot 2.83585 \dots^{21} - 1.54817 \dots \cdot 2.83585 \dots^{20} - 0.94956 \dots \cdot 2.83585 \dots^{19} - 1.46104 \dots \cdot 2.83585 \dots^{18} - 1.09346 \dots \cdot 2.83585 \dots^{17} - 1.42313 \dots \cdot 2.83585 \dots^{16} - 1.20092 \dots \cdot 2.83585 \dots^{15} - 1.41671 \dots \cdot 2.83585 \dots^{14} - 1.28609 \dots \cdot 2.83585 \dots^{13} - 1.43067 \dots \cdot 2.83585 \dots^{12} - 1.35787 \dots \cdot 2.83585 \dots^{11} - 1.45804 \dots \cdot 2.83585 \dots^{10} - 1.42186 \dots \cdot 2.83585 \dots^{9} - 1.49448 \dots \cdot 2.83585 \dots^{8} - 1.48163 \dots \cdot 2.83585 \dots^{7} - 1.53726 \dots \cdot 2.83585 \dots^{6} - 1.53940 \dots \cdot 2.83585 \dots^{5} - 1.58472 \dots \cdot 2.83585 \dots^{4} - 1.59663 \dots \cdot 2.83585 \dots^{3} - 1.63583 \dots \cdot 2.83585 \dots^{2} + 0.34576 \dots \cdot 2.83585 \dots - 1.24075 \dots = - 178371096387.3416

f^{^{'}} (u_{8}) = - 48 \cdot 2.83585 \dots^{23} - 10.33165 \dots \cdot 2.83585 \dots^{22} - 37.68185 \dots \cdot 2.83585 \dots^{21} - 15.68150 \dots \cdot 2.83585 \dots^{20} - 30.96351 \dots \cdot 2.83585 \dots^{19} - 18.04170 \dots \cdot 2.83585 \dots^{18} - 26.29873 \dots \cdot 2.83585 \dots^{17} - 18.58884 \dots \cdot 2.83585 \dots^{16} - 22.77013 \dots \cdot 2.83585 \dots^{15} - 18.01385 \dots \cdot 2.83585 \dots^{14} - 19.83404 \dots \cdot 2.83585 \dots^{13} - 16.71920 \dots \cdot 2.83585 \dots^{12} - 17.16810 \dots \cdot 2.83585 \dots^{11} - 14.93657 \dots \cdot 2.83585 \dots^{10} - 14.58046 \dots \cdot 2.83585 \dots^{9} - 12.79681 \dots \cdot 2.83585 \dots^{8} - 11.95584 \dots \cdot 2.83585 \dots^{7} - 10.37141 \dots \cdot 2.83585 \dots^{6} - 9.22360 \dots \cdot 2.83585 \dots^{5} - 7.69703 \dots \cdot 2.83585 \dots^{4} - 6.33891 \dots \cdot 2.83585 \dots^{3} - 4.78989 \dots \cdot 2.83585 \dots^{2} - 3.27166 \dots \cdot 2.83585 \dots + 0.34576 \dots = - 1488130184675.049

u_{9} = 2.71599 \dots

Δ u_{9} = ∣ 2.71599 \dots - 2.83585 \dots ∣ = 0.11986 \dots

Δ u_{9} = 0.11986 \dots

u_{10} = 2.60104 \dots : Δ u_{10} = 0.11495 \dots

f (u_{9}) = - 2 \cdot 2.71599 \dots^{24} - 0.44920 \dots \cdot 2.71599 \dots^{23} - 1.71281 \dots \cdot 2.71599 \dots^{22} - 0.74673 \dots \cdot 2.71599 \dots^{21} - 1.54817 \dots \cdot 2.71599 \dots^{20} - 0.94956 \dots \cdot 2.71599 \dots^{19} - 1.46104 \dots \cdot 2.71599 \dots^{18} - 1.09346 \dots \cdot 2.71599 \dots^{17} - 1.42313 \dots \cdot 2.71599 \dots^{16} - 1.20092 \dots \cdot 2.71599 \dots^{15} - 1.41671 \dots \cdot 2.71599 \dots^{14} - 1.28609 \dots \cdot 2.71599 \dots^{13} - 1.43067 \dots \cdot 2.71599 \dots^{12} - 1.35787 \dots \cdot 2.71599 \dots^{11} - 1.45804 \dots \cdot 2.71599 \dots^{10} - 1.42186 \dots \cdot 2.71599 \dots^{9} - 1.49448 \dots \cdot 2.71599 \dots^{8} - 1.48163 \dots \cdot 2.71599 \dots^{7} - 1.53726 \dots \cdot 2.71599 \dots^{6} - 1.53940 \dots \cdot 2.71599 \dots^{5} - 1.58472 \dots \cdot 2.71599 \dots^{4} - 1.59663 \dots \cdot 2.71599 \dots^{3} - 1.63583 \dots \cdot 2.71599 \dots^{2} + 0.34576 \dots \cdot 2.71599 \dots - 1.24075 \dots = - 64250912107.02736

f^{^{'}} (u_{9}) = - 48 \cdot 2.71599 \dots^{23} - 10.33165 \dots \cdot 2.71599 \dots^{22} - 37.68185 \dots \cdot 2.71599 \dots^{21} - 15.68150 \dots \cdot 2.71599 \dots^{20} - 30.96351 \dots \cdot 2.71599 \dots^{19} - 18.04170 \dots \cdot 2.71599 \dots^{18} - 26.29873 \dots \cdot 2.71599 \dots^{17} - 18.58884 \dots \cdot 2.71599 \dots^{16} - 22.77013 \dots \cdot 2.71599 \dots^{15} - 18.01385 \dots \cdot 2.71599 \dots^{14} - 19.83404 \dots \cdot 2.71599 \dots^{13} - 16.71920 \dots \cdot 2.71599 \dots^{12} - 17.16810 \dots \cdot 2.71599 \dots^{11} - 14.93657 \dots \cdot 2.71599 \dots^{10} - 14.58046 \dots \cdot 2.71599 \dots^{9} - 12.79681 \dots \cdot 2.71599 \dots^{8} - 11.95584 \dots \cdot 2.71599 \dots^{7} - 10.37141 \dots \cdot 2.71599 \dots^{6} - 9.22360 \dots \cdot 2.71599 \dots^{5} - 7.69703 \dots \cdot 2.71599 \dots^{4} - 6.33891 \dots \cdot 2.71599 \dots^{3} - 4.78989 \dots \cdot 2.71599 \dots^{2} - 3.27166 \dots \cdot 2.71599 \dots + 0.34576 \dots = - 558937953587.0385

u_{10} = 2.60104 \dots

Δ u_{10} = ∣ 2.60104 \dots - 2.71599 \dots ∣ = 0.11495 \dots

Δ u_{10} = 0.11495 \dots

u_{11} = 2.49078 \dots : Δ u_{11} = 0.11025 \dots

f (u_{10}) = - 2 \cdot 2.60104 \dots^{24} - 0.44920 \dots \cdot 2.60104 \dots^{23} - 1.71281 \dots \cdot 2.60104 \dots^{22} - 0.74673 \dots \cdot 2.60104 \dots^{21} - 1.54817 \dots \cdot 2.60104 \dots^{20} - 0.94956 \dots \cdot 2.60104 \dots^{19} - 1.46104 \dots \cdot 2.60104 \dots^{18} - 1.09346 \dots \cdot 2.60104 \dots^{17} - 1.42313 \dots \cdot 2.60104 \dots^{16} - 1.20092 \dots \cdot 2.60104 \dots^{15} - 1.41671 \dots \cdot 2.60104 \dots^{14} - 1.28609 \dots \cdot 2.60104 \dots^{13} - 1.43067 \dots \cdot 2.60104 \dots^{12} - 1.35787 \dots \cdot 2.60104 \dots^{11} - 1.45804 \dots \cdot 2.60104 \dots^{10} - 1.42186 \dots \cdot 2.60104 \dots^{9} - 1.49448 \dots \cdot 2.60104 \dots^{8} - 1.48163 \dots \cdot 2.60104 \dots^{7} - 1.53726 \dots \cdot 2.60104 \dots^{6} - 1.53940 \dots \cdot 2.60104 \dots^{5} - 1.58472 \dots \cdot 2.60104 \dots^{4} - 1.59663 \dots \cdot 2.60104 \dots^{3} - 1.63583 \dots \cdot 2.60104 \dots^{2} + 0.34576 \dots \cdot 2.60104 \dots - 1.24075 \dots = - 23144949417.36106

f^{^{'}} (u_{10}) = - 48 \cdot 2.60104 \dots^{23} - 10.33165 \dots \cdot 2.60104 \dots^{22} - 37.68185 \dots \cdot 2.60104 \dots^{21} - 15.68150 \dots \cdot 2.60104 \dots^{20} - 30.96351 \dots \cdot 2.60104 \dots^{19} - 18.04170 \dots \cdot 2.60104 \dots^{18} - 26.29873 \dots \cdot 2.60104 \dots^{17} - 18.58884 \dots \cdot 2.60104 \dots^{16} - 22.77013 \dots \cdot 2.60104 \dots^{15} - 18.01385 \dots \cdot 2.60104 \dots^{14} - 19.83404 \dots \cdot 2.60104 \dots^{13} - 16.71920 \dots \cdot 2.60104 \dots^{12} - 17.16810 \dots \cdot 2.60104 \dots^{11} - 14.93657 \dots \cdot 2.60104 \dots^{10} - 14.58046 \dots \cdot 2.60104 \dots^{9} - 12.79681 \dots \cdot 2.60104 \dots^{8} - 11.95584 \dots \cdot 2.60104 \dots^{7} - 10.37141 \dots \cdot 2.60104 \dots^{6} - 9.22360 \dots \cdot 2.60104 \dots^{5} - 7.69703 \dots \cdot 2.60104 \dots^{4} - 6.33891 \dots \cdot 2.60104 \dots^{3} - 4.78989 \dots \cdot 2.60104 \dots^{2} - 3.27166 \dots \cdot 2.60104 \dots + 0.34576 \dots = - 209924704239.2853

u_{11} = 2.49078 \dots

Δ u_{11} = ∣ 2.49078 \dots - 2.60104 \dots ∣ = 0.11025 \dots

Δ u_{11} = 0.11025 \dots

u_{12} = 2.38502 \dots : Δ u_{12} = 0.10576 \dots

f (u_{11}) = - 2 \cdot 2.49078 \dots^{24} - 0.44920 \dots \cdot 2.49078 \dots^{23} - 1.71281 \dots \cdot 2.49078 \dots^{22} - 0.74673 \dots \cdot 2.49078 \dots^{21} - 1.54817 \dots \cdot 2.49078 \dots^{20} - 0.94956 \dots \cdot 2.49078 \dots^{19} - 1.46104 \dots \cdot 2.49078 \dots^{18} - 1.09346 \dots \cdot 2.49078 \dots^{17} - 1.42313 \dots \cdot 2.49078 \dots^{16} - 1.20092 \dots \cdot 2.49078 \dots^{15} - 1.41671 \dots \cdot 2.49078 \dots^{14} - 1.28609 \dots \cdot 2.49078 \dots^{13} - 1.43067 \dots \cdot 2.49078 \dots^{12} - 1.35787 \dots \cdot 2.49078 \dots^{11} - 1.45804 \dots \cdot 2.49078 \dots^{10} - 1.42186 \dots \cdot 2.49078 \dots^{9} - 1.49448 \dots \cdot 2.49078 \dots^{8} - 1.48163 \dots \cdot 2.49078 \dots^{7} - 1.53726 \dots \cdot 2.49078 \dots^{6} - 1.53940 \dots \cdot 2.49078 \dots^{5} - 1.58472 \dots \cdot 2.49078 \dots^{4} - 1.59663 \dots \cdot 2.49078 \dots^{3} - 1.63583 \dots \cdot 2.49078 \dots^{2} + 0.34576 \dots \cdot 2.49078 \dots - 1.24075 \dots = - 8337950304.57477 \dots

f^{^{'}} (u_{11}) = - 48 \cdot 2.49078 \dots^{23} - 10.33165 \dots \cdot 2.49078 \dots^{22} - 37.68185 \dots \cdot 2.49078 \dots^{21} - 15.68150 \dots \cdot 2.49078 \dots^{20} - 30.96351 \dots \cdot 2.49078 \dots^{19} - 18.04170 \dots \cdot 2.49078 \dots^{18} - 26.29873 \dots \cdot 2.49078 \dots^{17} - 18.58884 \dots \cdot 2.49078 \dots^{16} - 22.77013 \dots \cdot 2.49078 \dots^{15} - 18.01385 \dots \cdot 2.49078 \dots^{14} - 19.83404 \dots \cdot 2.49078 \dots^{13} - 16.71920 \dots \cdot 2.49078 \dots^{12} - 17.16810 \dots \cdot 2.49078 \dots^{11} - 14.93657 \dots \cdot 2.49078 \dots^{10} - 14.58046 \dots \cdot 2.49078 \dots^{9} - 12.79681 \dots \cdot 2.49078 \dots^{8} - 11.95584 \dots \cdot 2.49078 \dots^{7} - 10.37141 \dots \cdot 2.49078 \dots^{6} - 9.22360 \dots \cdot 2.49078 \dots^{5} - 7.69703 \dots \cdot 2.49078 \dots^{4} - 6.33891 \dots \cdot 2.49078 \dots^{3} - 4.78989 \dots \cdot 2.49078 \dots^{2} - 3.27166 \dots \cdot 2.49078 \dots + 0.34576 \dots = - 78838181263.88246

u_{12} = 2.38502 \dots

Δ u_{12} = ∣ 2.38502 \dots - 2.49078 \dots ∣ = 0.10576 \dots

Δ u_{12} = 0.10576 \dots

u_{13} = 2.28356 \dots : Δ u_{13} = 0.10146 \dots

f (u_{12}) = - 2 \cdot 2.38502 \dots^{24} - 0.44920 \dots \cdot 2.38502 \dots^{23} - 1.71281 \dots \cdot 2.38502 \dots^{22} - 0.74673 \dots \cdot 2.38502 \dots^{21} - 1.54817 \dots \cdot 2.38502 \dots^{20} - 0.94956 \dots \cdot 2.38502 \dots^{19} - 1.46104 \dots \cdot 2.38502 \dots^{18} - 1.09346 \dots \cdot 2.38502 \dots^{17} - 1.42313 \dots \cdot 2.38502 \dots^{16} - 1.20092 \dots \cdot 2.38502 \dots^{15} - 1.41671 \dots \cdot 2.38502 \dots^{14} - 1.28609 \dots \cdot 2.38502 \dots^{13} - 1.43067 \dots \cdot 2.38502 \dots^{12} - 1.35787 \dots \cdot 2.38502 \dots^{11} - 1.45804 \dots \cdot 2.38502 \dots^{10} - 1.42186 \dots \cdot 2.38502 \dots^{9} - 1.49448 \dots \cdot 2.38502 \dots^{8} - 1.48163 \dots \cdot 2.38502 \dots^{7} - 1.53726 \dots \cdot 2.38502 \dots^{6} - 1.53940 \dots \cdot 2.38502 \dots^{5} - 1.58472 \dots \cdot 2.38502 \dots^{4} - 1.59663 \dots \cdot 2.38502 \dots^{3} - 1.63583 \dots \cdot 2.38502 \dots^{2} + 0.34576 \dots \cdot 2.38502 \dots - 1.24075 \dots = - 3003955170.83183 \dots

f^{^{'}} (u_{12}) = - 48 \cdot 2.38502 \dots^{23} - 10.33165 \dots \cdot 2.38502 \dots^{22} - 37.68185 \dots \cdot 2.38502 \dots^{21} - 15.68150 \dots \cdot 2.38502 \dots^{20} - 30.96351 \dots \cdot 2.38502 \dots^{19} - 18.04170 \dots \cdot 2.38502 \dots^{18} - 26.29873 \dots \cdot 2.38502 \dots^{17} - 18.58884 \dots \cdot 2.38502 \dots^{16} - 22.77013 \dots \cdot 2.38502 \dots^{15} - 18.01385 \dots \cdot 2.38502 \dots^{14} - 19.83404 \dots \cdot 2.38502 \dots^{13} - 16.71920 \dots \cdot 2.38502 \dots^{12} - 17.16810 \dots \cdot 2.38502 \dots^{11} - 14.93657 \dots \cdot 2.38502 \dots^{10} - 14.58046 \dots \cdot 2.38502 \dots^{9} - 12.79681 \dots \cdot 2.38502 \dots^{8} - 11.95584 \dots \cdot 2.38502 \dots^{7} - 10.37141 \dots \cdot 2.38502 \dots^{6} - 9.22360 \dots \cdot 2.38502 \dots^{5} - 7.69703 \dots \cdot 2.38502 \dots^{4} - 6.33891 \dots \cdot 2.38502 \dots^{3} - 4.78989 \dots \cdot 2.38502 \dots^{2} - 3.27166 \dots \cdot 2.38502 \dots + 0.34576 \dots = - 29605851650.56715

u_{13} = 2.28356 \dots

Δ u_{13} = ∣ 2.28356 \dots - 2.38502 \dots ∣ = 0.10146 \dots

Δ u_{13} = 0.10146 \dots

u_{14} = 2.18620 \dots : Δ u_{14} = 0.09736 \dots

f (u_{13}) = - 2 \cdot 2.28356 \dots^{24} - 0.44920 \dots \cdot 2.28356 \dots^{23} - 1.71281 \dots \cdot 2.28356 \dots^{22} - 0.74673 \dots \cdot 2.28356 \dots^{21} - 1.54817 \dots \cdot 2.28356 \dots^{20} - 0.94956 \dots \cdot 2.28356 \dots^{19} - 1.46104 \dots \cdot 2.28356 \dots^{18} - 1.09346 \dots \cdot 2.28356 \dots^{17} - 1.42313 \dots \cdot 2.28356 \dots^{16} - 1.20092 \dots \cdot 2.28356 \dots^{15} - 1.41671 \dots \cdot 2.28356 \dots^{14} - 1.28609 \dots \cdot 2.28356 \dots^{13} - 1.43067 \dots \cdot 2.28356 \dots^{12} - 1.35787 \dots \cdot 2.28356 \dots^{11} - 1.45804 \dots \cdot 2.28356 \dots^{10} - 1.42186 \dots \cdot 2.28356 \dots^{9} - 1.49448 \dots \cdot 2.28356 \dots^{8} - 1.48163 \dots \cdot 2.28356 \dots^{7} - 1.53726 \dots \cdot 2.28356 \dots^{6} - 1.53940 \dots \cdot 2.28356 \dots^{5} - 1.58472 \dots \cdot 2.28356 \dots^{4} - 1.59663 \dots \cdot 2.28356 \dots^{3} - 1.63583 \dots \cdot 2.28356 \dots^{2} + 0.34576 \dots \cdot 2.28356 \dots - 1.24075 \dots = - 1082342857.68191 \dots

f^{^{'}} (u_{13}) = - 48 \cdot 2.28356 \dots^{23} - 10.33165 \dots \cdot 2.28356 \dots^{22} - 37.68185 \dots \cdot 2.28356 \dots^{21} - 15.68150 \dots \cdot 2.28356 \dots^{20} - 30.96351 \dots \cdot 2.28356 \dots^{19} - 18.04170 \dots \cdot 2.28356 \dots^{18} - 26.29873 \dots \cdot 2.28356 \dots^{17} - 18.58884 \dots \cdot 2.28356 \dots^{16} - 22.77013 \dots \cdot 2.28356 \dots^{15} - 18.01385 \dots \cdot 2.28356 \dots^{14} - 19.83404 \dots \cdot 2.28356 \dots^{13} - 16.71920 \dots \cdot 2.28356 \dots^{12} - 17.16810 \dots \cdot 2.28356 \dots^{11} - 14.93657 \dots \cdot 2.28356 \dots^{10} - 14.58046 \dots \cdot 2.28356 \dots^{9} - 12.79681 \dots \cdot 2.28356 \dots^{8} - 11.95584 \dots \cdot 2.28356 \dots^{7} - 10.37141 \dots \cdot 2.28356 \dots^{6} - 9.22360 \dots \cdot 2.28356 \dots^{5} - 7.69703 \dots \cdot 2.28356 \dots^{4} - 6.33891 \dots \cdot 2.28356 \dots^{3} - 4.78989 \dots \cdot 2.28356 \dots^{2} - 3.27166 \dots \cdot 2.28356 \dots + 0.34576 \dots = - 11116803664.87232

u_{14} = 2.18620 \dots

Δ u_{14} = ∣ 2.18620 \dots - 2.28356 \dots ∣ = 0.09736 \dots

Δ u_{14} = 0.09736 \dots

u_{15} = 2.09275 \dots : Δ u_{15} = 0.09344 \dots

f (u_{14}) = - 2 \cdot 2.18620 \dots^{24} - 0.44920 \dots \cdot 2.18620 \dots^{23} - 1.71281 \dots \cdot 2.18620 \dots^{22} - 0.74673 \dots \cdot 2.18620 \dots^{21} - 1.54817 \dots \cdot 2.18620 \dots^{20} - 0.94956 \dots \cdot 2.18620 \dots^{19} - 1.46104 \dots \cdot 2.18620 \dots^{18} - 1.09346 \dots \cdot 2.18620 \dots^{17} - 1.42313 \dots \cdot 2.18620 \dots^{16} - 1.20092 \dots \cdot 2.18620 \dots^{15} - 1.41671 \dots \cdot 2.18620 \dots^{14} - 1.28609 \dots \cdot 2.18620 \dots^{13} - 1.43067 \dots \cdot 2.18620 \dots^{12} - 1.35787 \dots \cdot 2.18620 \dots^{11} - 1.45804 \dots \cdot 2.18620 \dots^{10} - 1.42186 \dots \cdot 2.18620 \dots^{9} - 1.49448 \dots \cdot 2.18620 \dots^{8} - 1.48163 \dots \cdot 2.18620 \dots^{7} - 1.53726 \dots \cdot 2.18620 \dots^{6} - 1.53940 \dots \cdot 2.18620 \dots^{5} - 1.58472 \dots \cdot 2.18620 \dots^{4} - 1.59663 \dots \cdot 2.18620 \dots^{3} - 1.63583 \dots \cdot 2.18620 \dots^{2} + 0.34576 \dots \cdot 2.18620 \dots - 1.24075 \dots = - 390015030.27114 \dots

f^{^{'}} (u_{14}) = - 48 \cdot 2.18620 \dots^{23} - 10.33165 \dots \cdot 2.18620 \dots^{22} - 37.68185 \dots \cdot 2.18620 \dots^{21} - 15.68150 \dots \cdot 2.18620 \dots^{20} - 30.96351 \dots \cdot 2.18620 \dots^{19} - 18.04170 \dots \cdot 2.18620 \dots^{18} - 26.29873 \dots \cdot 2.18620 \dots^{17} - 18.58884 \dots \cdot 2.18620 \dots^{16} - 22.77013 \dots \cdot 2.18620 \dots^{15} - 18.01385 \dots \cdot 2.18620 \dots^{14} - 19.83404 \dots \cdot 2.18620 \dots^{13} - 16.71920 \dots \cdot 2.18620 \dots^{12} - 17.16810 \dots \cdot 2.18620 \dots^{11} - 14.93657 \dots \cdot 2.18620 \dots^{10} - 14.58046 \dots \cdot 2.18620 \dots^{9} - 12.79681 \dots \cdot 2.18620 \dots^{8} - 11.95584 \dots \cdot 2.18620 \dots^{7} - 10.37141 \dots \cdot 2.18620 \dots^{6} - 9.22360 \dots \cdot 2.18620 \dots^{5} - 7.69703 \dots \cdot 2.18620 \dots^{4} - 6.33891 \dots \cdot 2.18620 \dots^{3} - 4.78989 \dots \cdot 2.18620 \dots^{2} - 3.27166 \dots \cdot 2.18620 \dots + 0.34576 \dots = - 4173836931.61639 \dots

u_{15} = 2.09275 \dots

Δ u_{15} = ∣ 2.09275 \dots - 2.18620 \dots ∣ = 0.09344 \dots

Δ u_{15} = 0.09344 \dots

u_{16} = 2.00305 \dots : Δ u_{16} = 0.08970 \dots

f (u_{15}) = - 2 \cdot 2.09275 \dots^{24} - 0.44920 \dots \cdot 2.09275 \dots^{23} - 1.71281 \dots \cdot 2.09275 \dots^{22} - 0.74673 \dots \cdot 2.09275 \dots^{21} - 1.54817 \dots \cdot 2.09275 \dots^{20} - 0.94956 \dots \cdot 2.09275 \dots^{19} - 1.46104 \dots \cdot 2.09275 \dots^{18} - 1.09346 \dots \cdot 2.09275 \dots^{17} - 1.42313 \dots \cdot 2.09275 \dots^{16} - 1.20092 \dots \cdot 2.09275 \dots^{15} - 1.41671 \dots \cdot 2.09275 \dots^{14} - 1.28609 \dots \cdot 2.09275 \dots^{13} - 1.43067 \dots \cdot 2.09275 \dots^{12} - 1.35787 \dots \cdot 2.09275 \dots^{11} - 1.45804 \dots \cdot 2.09275 \dots^{10} - 1.42186 \dots \cdot 2.09275 \dots^{9} - 1.49448 \dots \cdot 2.09275 \dots^{8} - 1.48163 \dots \cdot 2.09275 \dots^{7} - 1.53726 \dots \cdot 2.09275 \dots^{6} - 1.53940 \dots \cdot 2.09275 \dots^{5} - 1.58472 \dots \cdot 2.09275 \dots^{4} - 1.59663 \dots \cdot 2.09275 \dots^{3} - 1.63583 \dots \cdot 2.09275 \dots^{2} + 0.34576 \dots \cdot 2.09275 \dots - 1.24075 \dots = - 140557142.73149 \dots

f^{^{'}} (u_{15}) = - 48 \cdot 2.09275 \dots^{23} - 10.33165 \dots \cdot 2.09275 \dots^{22} - 37.68185 \dots \cdot 2.09275 \dots^{21} - 15.68150 \dots \cdot 2.09275 \dots^{20} - 30.96351 \dots \cdot 2.09275 \dots^{19} - 18.04170 \dots \cdot 2.09275 \dots^{18} - 26.29873 \dots \cdot 2.09275 \dots^{17} - 18.58884 \dots \cdot 2.09275 \dots^{16} - 22.77013 \dots \cdot 2.09275 \dots^{15} - 18.01385 \dots \cdot 2.09275 \dots^{14} - 19.83404 \dots \cdot 2.09275 \dots^{13} - 16.71920 \dots \cdot 2.09275 \dots^{12} - 17.16810 \dots \cdot 2.09275 \dots^{11} - 14.93657 \dots \cdot 2.09275 \dots^{10} - 14.58046 \dots \cdot 2.09275 \dots^{9} - 12.79681 \dots \cdot 2.09275 \dots^{8} - 11.95584 \dots \cdot 2.09275 \dots^{7} - 10.37141 \dots \cdot 2.09275 \dots^{6} - 9.22360 \dots \cdot 2.09275 \dots^{5} - 7.69703 \dots \cdot 2.09275 \dots^{4} - 6.33891 \dots \cdot 2.09275 \dots^{3} - 4.78989 \dots \cdot 2.09275 \dots^{2} - 3.27166 \dots \cdot 2.09275 \dots + 0.34576 \dots = - 1566872179.68956 \dots

u_{16} = 2.00305 \dots

Δ u_{16} = ∣ 2.00305 \dots - 2.09275 \dots ∣ = 0.08970 \dots

Δ u_{16} = 0.08970 \dots

u_{17} = 1.91690 \dots : Δ u_{17} = 0.08614 \dots

f (u_{16}) = - 2 \cdot 2.00305 \dots^{24} - 0.44920 \dots \cdot 2.00305 \dots^{23} - 1.71281 \dots \cdot 2.00305 \dots^{22} - 0.74673 \dots \cdot 2.00305 \dots^{21} - 1.54817 \dots \cdot 2.00305 \dots^{20} - 0.94956 \dots \cdot 2.00305 \dots^{19} - 1.46104 \dots \cdot 2.00305 \dots^{18} - 1.09346 \dots \cdot 2.00305 \dots^{17} - 1.42313 \dots \cdot 2.00305 \dots^{16} - 1.20092 \dots \cdot 2.00305 \dots^{15} - 1.41671 \dots \cdot 2.00305 \dots^{14} - 1.28609 \dots \cdot 2.00305 \dots^{13} - 1.43067 \dots \cdot 2.00305 \dots^{12} - 1.35787 \dots \cdot 2.00305 \dots^{11} - 1.45804 \dots \cdot 2.00305 \dots^{10} - 1.42186 \dots \cdot 2.00305 \dots^{9} - 1.49448 \dots \cdot 2.00305 \dots^{8} - 1.48163 \dots \cdot 2.00305 \dots^{7} - 1.53726 \dots \cdot 2.00305 \dots^{6} - 1.53940 \dots \cdot 2.00305 \dots^{5} - 1.58472 \dots \cdot 2.00305 \dots^{4} - 1.59663 \dots \cdot 2.00305 \dots^{3} - 1.63583 \dots \cdot 2.00305 \dots^{2} + 0.34576 \dots \cdot 2.00305 \dots - 1.24075 \dots = - 50663196.21701 \dots

f^{^{'}} (u_{16}) = - 48 \cdot 2.00305 \dots^{23} - 10.33165 \dots \cdot 2.00305 \dots^{22} - 37.68185 \dots \cdot 2.00305 \dots^{21} - 15.68150 \dots \cdot 2.00305 \dots^{20} - 30.96351 \dots \cdot 2.00305 \dots^{19} - 18.04170 \dots \cdot 2.00305 \dots^{18} - 26.29873 \dots \cdot 2.00305 \dots^{17} - 18.58884 \dots \cdot 2.00305 \dots^{16} - 22.77013 \dots \cdot 2.00305 \dots^{15} - 18.01385 \dots \cdot 2.00305 \dots^{14} - 19.83404 \dots \cdot 2.00305 \dots^{13} - 16.71920 \dots \cdot 2.00305 \dots^{12} - 17.16810 \dots \cdot 2.00305 \dots^{11} - 14.93657 \dots \cdot 2.00305 \dots^{10} - 14.58046 \dots \cdot 2.00305 \dots^{9} - 12.79681 \dots \cdot 2.00305 \dots^{8} - 11.95584 \dots \cdot 2.00305 \dots^{7} - 10.37141 \dots \cdot 2.00305 \dots^{6} - 9.22360 \dots \cdot 2.00305 \dots^{5} - 7.69703 \dots \cdot 2.00305 \dots^{4} - 6.33891 \dots \cdot 2.00305 \dots^{3} - 4.78989 \dots \cdot 2.00305 \dots^{2} - 3.27166 \dots \cdot 2.00305 \dots + 0.34576 \dots = - 588112411.70776 \dots

u_{17} = 1.91690 \dots

Δ u_{17} = ∣ 1.91690 \dots - 2.00305 \dots ∣ = 0.08614 \dots

Δ u_{17} = 0.08614 \dots

u_{18} = 1.83414 \dots : Δ u_{18} = 0.08275 \dots

f (u_{17}) = - 2 \cdot 1.91690 \dots^{24} - 0.44920 \dots \cdot 1.91690 \dots^{23} - 1.71281 \dots \cdot 1.91690 \dots^{22} - 0.74673 \dots \cdot 1.91690 \dots^{21} - 1.54817 \dots \cdot 1.91690 \dots^{20} - 0.94956 \dots \cdot 1.91690 \dots^{19} - 1.46104 \dots \cdot 1.91690 \dots^{18} - 1.09346 \dots \cdot 1.91690 \dots^{17} - 1.42313 \dots \cdot 1.91690 \dots^{16} - 1.20092 \dots \cdot 1.91690 \dots^{15} - 1.41671 \dots \cdot 1.91690 \dots^{14} - 1.28609 \dots \cdot 1.91690 \dots^{13} - 1.43067 \dots \cdot 1.91690 \dots^{12} - 1.35787 \dots \cdot 1.91690 \dots^{11} - 1.45804 \dots \cdot 1.91690 \dots^{10} - 1.42186 \dots \cdot 1.91690 \dots^{9} - 1.49448 \dots \cdot 1.91690 \dots^{8} - 1.48163 \dots \cdot 1.91690 \dots^{7} - 1.53726 \dots \cdot 1.91690 \dots^{6} - 1.53940 \dots \cdot 1.91690 \dots^{5} - 1.58472 \dots \cdot 1.91690 \dots^{4} - 1.59663 \dots \cdot 1.91690 \dots^{3} - 1.63583 \dots \cdot 1.91690 \dots^{2} + 0.34576 \dots \cdot 1.91690 \dots - 1.24075 \dots = - 18264908.81934 \dots

f^{^{'}} (u_{17}) = - 48 \cdot 1.91690 \dots^{23} - 10.33165 \dots \cdot 1.91690 \dots^{22} - 37.68185 \dots \cdot 1.91690 \dots^{21} - 15.68150 \dots \cdot 1.91690 \dots^{20} - 30.96351 \dots \cdot 1.91690 \dots^{19} - 18.04170 \dots \cdot 1.91690 \dots^{18} - 26.29873 \dots \cdot 1.91690 \dots^{17} - 18.58884 \dots \cdot 1.91690 \dots^{16} - 22.77013 \dots \cdot 1.91690 \dots^{15} - 18.01385 \dots \cdot 1.91690 \dots^{14} - 19.83404 \dots \cdot 1.91690 \dots^{13} - 16.71920 \dots \cdot 1.91690 \dots^{12} - 17.16810 \dots \cdot 1.91690 \dots^{11} - 14.93657 \dots \cdot 1.91690 \dots^{10} - 14.58046 \dots \cdot 1.91690 \dots^{9} - 12.79681 \dots \cdot 1.91690 \dots^{8} - 11.95584 \dots \cdot 1.91690 \dots^{7} - 10.37141 \dots \cdot 1.91690 \dots^{6} - 9.22360 \dots \cdot 1.91690 \dots^{5} - 7.69703 \dots \cdot 1.91690 \dots^{4} - 6.33891 \dots \cdot 1.91690 \dots^{3} - 4.78989 \dots \cdot 1.91690 \dots^{2} - 3.27166 \dots \cdot 1.91690 \dots + 0.34576 \dots = - 220697479.49118 \dots

u_{18} = 1.83414 \dots

Δ u_{18} = ∣ 1.83414 \dots - 1.91690 \dots ∣ = 0.08275 \dots

Δ u_{18} = 0.08275 \dots

u_{19} = 1.75459 \dots : Δ u_{19} = 0.07954 \dots

f (u_{18}) = - 2 \cdot 1.83414 \dots^{24} - 0.44920 \dots \cdot 1.83414 \dots^{23} - 1.71281 \dots \cdot 1.83414 \dots^{22} - 0.74673 \dots \cdot 1.83414 \dots^{21} - 1.54817 \dots \cdot 1.83414 \dots^{20} - 0.94956 \dots \cdot 1.83414 \dots^{19} - 1.46104 \dots \cdot 1.83414 \dots^{18} - 1.09346 \dots \cdot 1.83414 \dots^{17} - 1.42313 \dots \cdot 1.83414 \dots^{16} - 1.20092 \dots \cdot 1.83414 \dots^{15} - 1.41671 \dots \cdot 1.83414 \dots^{14} - 1.28609 \dots \cdot 1.83414 \dots^{13} - 1.43067 \dots \cdot 1.83414 \dots^{12} - 1.35787 \dots \cdot 1.83414 \dots^{11} - 1.45804 \dots \cdot 1.83414 \dots^{10} - 1.42186 \dots \cdot 1.83414 \dots^{9} - 1.49448 \dots \cdot 1.83414 \dots^{8} - 1.48163 \dots \cdot 1.83414 \dots^{7} - 1.53726 \dots \cdot 1.83414 \dots^{6} - 1.53940 \dots \cdot 1.83414 \dots^{5} - 1.58472 \dots \cdot 1.83414 \dots^{4} - 1.59663 \dots \cdot 1.83414 \dots^{3} - 1.63583 \dots \cdot 1.83414 \dots^{2} + 0.34576 \dots \cdot 1.83414 \dots - 1.24075 \dots = - 6586440.85241 \dots

f^{^{'}} (u_{18}) = - 48 \cdot 1.83414 \dots^{23} - 10.33165 \dots \cdot 1.83414 \dots^{22} - 37.68185 \dots \cdot 1.83414 \dots^{21} - 15.68150 \dots \cdot 1.83414 \dots^{20} - 30.96351 \dots \cdot 1.83414 \dots^{19} - 18.04170 \dots \cdot 1.83414 \dots^{18} - 26.29873 \dots \cdot 1.83414 \dots^{17} - 18.58884 \dots \cdot 1.83414 \dots^{16} - 22.77013 \dots \cdot 1.83414 \dots^{15} - 18.01385 \dots \cdot 1.83414 \dots^{14} - 19.83404 \dots \cdot 1.83414 \dots^{13} - 16.71920 \dots \cdot 1.83414 \dots^{12} - 17.16810 \dots \cdot 1.83414 \dots^{11} - 14.93657 \dots \cdot 1.83414 \dots^{10} - 14.58046 \dots \cdot 1.83414 \dots^{9} - 12.79681 \dots \cdot 1.83414 \dots^{8} - 11.95584 \dots \cdot 1.83414 \dots^{7} - 10.37141 \dots \cdot 1.83414 \dots^{6} - 9.22360 \dots \cdot 1.83414 \dots^{5} - 7.69703 \dots \cdot 1.83414 \dots^{4} - 6.33891 \dots \cdot 1.83414 \dots^{3} - 4.78989 \dots \cdot 1.83414 \dots^{2} - 3.27166 \dots \cdot 1.83414 \dots + 0.34576 \dots = - 82797966.86806 \dots

u_{19} = 1.75459 \dots

Δ u_{19} = ∣ 1.75459 \dots - 1.83414 \dots ∣ = 0.07954 \dots

Δ u_{19} = 0.07954 \dots

u_{20} = 1.67808 \dots : Δ u_{20} = 0.07651 \dots

f (u_{19}) = - 2 \cdot 1.75459 \dots^{24} - 0.44920 \dots \cdot 1.75459 \dots^{23} - 1.71281 \dots \cdot 1.75459 \dots^{22} - 0.74673 \dots \cdot 1.75459 \dots^{21} - 1.54817 \dots \cdot 1.75459 \dots^{20} - 0.94956 \dots \cdot 1.75459 \dots^{19} - 1.46104 \dots \cdot 1.75459 \dots^{18} - 1.09346 \dots \cdot 1.75459 \dots^{17} - 1.42313 \dots \cdot 1.75459 \dots^{16} - 1.20092 \dots \cdot 1.75459 \dots^{15} - 1.41671 \dots \cdot 1.75459 \dots^{14} - 1.28609 \dots \cdot 1.75459 \dots^{13} - 1.43067 \dots \cdot 1.75459 \dots^{12} - 1.35787 \dots \cdot 1.75459 \dots^{11} - 1.45804 \dots \cdot 1.75459 \dots^{10} - 1.42186 \dots \cdot 1.75459 \dots^{9} - 1.49448 \dots \cdot 1.75459 \dots^{8} - 1.48163 \dots \cdot 1.75459 \dots^{7} - 1.53726 \dots \cdot 1.75459 \dots^{6} - 1.53940 \dots \cdot 1.75459 \dots^{5} - 1.58472 \dots \cdot 1.75459 \dots^{4} - 1.59663 \dots \cdot 1.75459 \dots^{3} - 1.63583 \dots \cdot 1.75459 \dots^{2} + 0.34576 \dots \cdot 1.75459 \dots - 1.24075 \dots = - 2375878.39528 \dots

f^{^{'}} (u_{19}) = - 48 \cdot 1.75459 \dots^{23} - 10.33165 \dots \cdot 1.75459 \dots^{22} - 37.68185 \dots \cdot 1.75459 \dots^{21} - 15.68150 \dots \cdot 1.75459 \dots^{20} - 30.96351 \dots \cdot 1.75459 \dots^{19} - 18.04170 \dots \cdot 1.75459 \dots^{18} - 26.29873 \dots \cdot 1.75459 \dots^{17} - 18.58884 \dots \cdot 1.75459 \dots^{16} - 22.77013 \dots \cdot 1.75459 \dots^{15} - 18.01385 \dots \cdot 1.75459 \dots^{14} - 19.83404 \dots \cdot 1.75459 \dots^{13} - 16.71920 \dots \cdot 1.75459 \dots^{12} - 17.16810 \dots \cdot 1.75459 \dots^{11} - 14.93657 \dots \cdot 1.75459 \dots^{10} - 14.58046 \dots \cdot 1.75459 \dots^{9} - 12.79681 \dots \cdot 1.75459 \dots^{8} - 11.95584 \dots \cdot 1.75459 \dots^{7} - 10.37141 \dots \cdot 1.75459 \dots^{6} - 9.22360 \dots \cdot 1.75459 \dots^{5} - 7.69703 \dots \cdot 1.75459 \dots^{4} - 6.33891 \dots \cdot 1.75459 \dots^{3} - 4.78989 \dots \cdot 1.75459 \dots^{2} - 3.27166 \dots \cdot 1.75459 \dots + 0.34576 \dots = - 31052217.21882 \dots

u_{20} = 1.67808 \dots

Δ u_{20} = ∣ 1.67808 \dots - 1.75459 \dots ∣ = 0.07651 \dots

Δ u_{20} = 0.07651 \dots

u_{21} = 1.60442 \dots : Δ u_{21} = 0.07365 \dots

f (u_{20}) = - 2 \cdot 1.67808 \dots^{24} - 0.44920 \dots \cdot 1.67808 \dots^{23} - 1.71281 \dots \cdot 1.67808 \dots^{22} - 0.74673 \dots \cdot 1.67808 \dots^{21} - 1.54817 \dots \cdot 1.67808 \dots^{20} - 0.94956 \dots \cdot 1.67808 \dots^{19} - 1.46104 \dots \cdot 1.67808 \dots^{18} - 1.09346 \dots \cdot 1.67808 \dots^{17} - 1.42313 \dots \cdot 1.67808 \dots^{16} - 1.20092 \dots \cdot 1.67808 \dots^{15} - 1.41671 \dots \cdot 1.67808 \dots^{14} - 1.28609 \dots \cdot 1.67808 \dots^{13} - 1.43067 \dots \cdot 1.67808 \dots^{12} - 1.35787 \dots \cdot 1.67808 \dots^{11} - 1.45804 \dots \cdot 1.67808 \dots^{10} - 1.42186 \dots \cdot 1.67808 \dots^{9} - 1.49448 \dots \cdot 1.67808 \dots^{8} - 1.48163 \dots \cdot 1.67808 \dots^{7} - 1.53726 \dots \cdot 1.67808 \dots^{6} - 1.53940 \dots \cdot 1.67808 \dots^{5} - 1.58472 \dots \cdot 1.67808 \dots^{4} - 1.59663 \dots \cdot 1.67808 \dots^{3} - 1.63583 \dots \cdot 1.67808 \dots^{2} + 0.34576 \dots \cdot 1.67808 \dots - 1.24075 \dots = - 857398.01456 \dots

f^{^{'}} (u_{20}) = - 48 \cdot 1.67808 \dots^{23} - 10.33165 \dots \cdot 1.67808 \dots^{22} - 37.68185 \dots \cdot 1.67808 \dots^{21} - 15.68150 \dots \cdot 1.67808 \dots^{20} - 30.96351 \dots \cdot 1.67808 \dots^{19} - 18.04170 \dots \cdot 1.67808 \dots^{18} - 26.29873 \dots \cdot 1.67808 \dots^{17} - 18.58884 \dots \cdot 1.67808 \dots^{16} - 22.77013 \dots \cdot 1.67808 \dots^{15} - 18.01385 \dots \cdot 1.67808 \dots^{14} - 19.83404 \dots \cdot 1.67808 \dots^{13} - 16.71920 \dots \cdot 1.67808 \dots^{12} - 17.16810 \dots \cdot 1.67808 \dots^{11} - 14.93657 \dots \cdot 1.67808 \dots^{10} - 14.58046 \dots \cdot 1.67808 \dots^{9} - 12.79681 \dots \cdot 1.67808 \dots^{8} - 11.95584 \dots \cdot 1.67808 \dots^{7} - 10.37141 \dots \cdot 1.67808 \dots^{6} - 9.22360 \dots \cdot 1.67808 \dots^{5} - 7.69703 \dots \cdot 1.67808 \dots^{4} - 6.33891 \dots \cdot 1.67808 \dots^{3} - 4.78989 \dots \cdot 1.67808 \dots^{2} - 3.27166 \dots \cdot 1.67808 \dots + 0.34576 \dots = - 11640374.89691 \dots

u_{21} = 1.60442 \dots

Δ u_{21} = ∣ 1.60442 \dots - 1.67808 \dots ∣ = 0.07365 \dots

Δ u_{21} = 0.07365 \dots

u_{22} = 1.53343 \dots : Δ u_{22} = 0.07099 \dots

f (u_{21}) = - 2 \cdot 1.60442 \dots^{24} - 0.44920 \dots \cdot 1.60442 \dots^{23} - 1.71281 \dots \cdot 1.60442 \dots^{22} - 0.74673 \dots \cdot 1.60442 \dots^{21} - 1.54817 \dots \cdot 1.60442 \dots^{20} - 0.94956 \dots \cdot 1.60442 \dots^{19} - 1.46104 \dots \cdot 1.60442 \dots^{18} - 1.09346 \dots \cdot 1.60442 \dots^{17} - 1.42313 \dots \cdot 1.60442 \dots^{16} - 1.20092 \dots \cdot 1.60442 \dots^{15} - 1.41671 \dots \cdot 1.60442 \dots^{14} - 1.28609 \dots \cdot 1.60442 \dots^{13} - 1.43067 \dots \cdot 1.60442 \dots^{12} - 1.35787 \dots \cdot 1.60442 \dots^{11} - 1.45804 \dots \cdot 1.60442 \dots^{10} - 1.42186 \dots \cdot 1.60442 \dots^{9} - 1.49448 \dots \cdot 1.60442 \dots^{8} - 1.48163 \dots \cdot 1.60442 \dots^{7} - 1.53726 \dots \cdot 1.60442 \dots^{6} - 1.53940 \dots \cdot 1.60442 \dots^{5} - 1.58472 \dots \cdot 1.60442 \dots^{4} - 1.59663 \dots \cdot 1.60442 \dots^{3} - 1.63583 \dots \cdot 1.60442 \dots^{2} + 0.34576 \dots \cdot 1.60442 \dots - 1.24075 \dots = - 309592.42704 \dots

f^{^{'}} (u_{21}) = - 48 \cdot 1.60442 \dots^{23} - 10.33165 \dots \cdot 1.60442 \dots^{22} - 37.68185 \dots \cdot 1.60442 \dots^{21} - 15.68150 \dots \cdot 1.60442 \dots^{20} - 30.96351 \dots \cdot 1.60442 \dots^{19} - 18.04170 \dots \cdot 1.60442 \dots^{18} - 26.29873 \dots \cdot 1.60442 \dots^{17} - 18.58884 \dots \cdot 1.60442 \dots^{16} - 22.77013 \dots \cdot 1.60442 \dots^{15} - 18.01385 \dots \cdot 1.60442 \dots^{14} - 19.83404 \dots \cdot 1.60442 \dots^{13} - 16.71920 \dots \cdot 1.60442 \dots^{12} - 17.16810 \dots \cdot 1.60442 \dots^{11} - 14.93657 \dots \cdot 1.60442 \dots^{10} - 14.58046 \dots \cdot 1.60442 \dots^{9} - 12.79681 \dots \cdot 1.60442 \dots^{8} - 11.95584 \dots \cdot 1.60442 \dots^{7} - 10.37141 \dots \cdot 1.60442 \dots^{6} - 9.22360 \dots \cdot 1.60442 \dots^{5} - 7.69703 \dots \cdot 1.60442 \dots^{4} - 6.33891 \dots \cdot 1.60442 \dots^{3} - 4.78989 \dots \cdot 1.60442 \dots^{2} - 3.27166 \dots \cdot 1.60442 \dots + 0.34576 \dots = - 4360845.39742 \dots

u_{22} = 1.53343 \dots

Δ u_{22} = ∣ 1.53343 \dots - 1.60442 \dots ∣ = 0.07099 \dots

Δ u_{22} = 0.07099 \dots

u_{23} = 1.46489 \dots : Δ u_{23} = 0.06854 \dots

f (u_{22}) = - 2 \cdot 1.53343 \dots^{24} - 0.44920 \dots \cdot 1.53343 \dots^{23} - 1.71281 \dots \cdot 1.53343 \dots^{22} - 0.74673 \dots \cdot 1.53343 \dots^{21} - 1.54817 \dots \cdot 1.53343 \dots^{20} - 0.94956 \dots \cdot 1.53343 \dots^{19} - 1.46104 \dots \cdot 1.53343 \dots^{18} - 1.09346 \dots \cdot 1.53343 \dots^{17} - 1.42313 \dots \cdot 1.53343 \dots^{16} - 1.20092 \dots \cdot 1.53343 \dots^{15} - 1.41671 \dots \cdot 1.53343 \dots^{14} - 1.28609 \dots \cdot 1.53343 \dots^{13} - 1.43067 \dots \cdot 1.53343 \dots^{12} - 1.35787 \dots \cdot 1.53343 \dots^{11} - 1.45804 \dots \cdot 1.53343 \dots^{10} - 1.42186 \dots \cdot 1.53343 \dots^{9} - 1.49448 \dots \cdot 1.53343 \dots^{8} - 1.48163 \dots \cdot 1.53343 \dots^{7} - 1.53726 \dots \cdot 1.53343 \dots^{6} - 1.53940 \dots \cdot 1.53343 \dots^{5} - 1.58472 \dots \cdot 1.53343 \dots^{4} - 1.59663 \dots \cdot 1.53343 \dots^{3} - 1.63583 \dots \cdot 1.53343 \dots^{2} + 0.34576 \dots \cdot 1.53343 \dots - 1.24075 \dots = - 111877.91739 \dots

f^{^{'}} (u_{22}) = - 48 \cdot 1.53343 \dots^{23} - 10.33165 \dots \cdot 1.53343 \dots^{22} - 37.68185 \dots \cdot 1.53343 \dots^{21} - 15.68150 \dots \cdot 1.53343 \dots^{20} - 30.96351 \dots \cdot 1.53343 \dots^{19} - 18.04170 \dots \cdot 1.53343 \dots^{18} - 26.29873 \dots \cdot 1.53343 \dots^{17} - 18.58884 \dots \cdot 1.53343 \dots^{16} - 22.77013 \dots \cdot 1.53343 \dots^{15} - 18.01385 \dots \cdot 1.53343 \dots^{14} - 19.83404 \dots \cdot 1.53343 \dots^{13} - 16.71920 \dots \cdot 1.53343 \dots^{12} - 17.16810 \dots \cdot 1.53343 \dots^{11} - 14.93657 \dots \cdot 1.53343 \dots^{10} - 14.58046 \dots \cdot 1.53343 \dots^{9} - 12.79681 \dots \cdot 1.53343 \dots^{8} - 11.95584 \dots \cdot 1.53343 \dots^{7} - 10.37141 \dots \cdot 1.53343 \dots^{6} - 9.22360 \dots \cdot 1.53343 \dots^{5} - 7.69703 \dots \cdot 1.53343 \dots^{4} - 6.33891 \dots \cdot 1.53343 \dots^{3} - 4.78989 \dots \cdot 1.53343 \dots^{2} - 3.27166 \dots \cdot 1.53343 \dots + 0.34576 \dots = - 1632281.12839 \dots

u_{23} = 1.46489 \dots

Δ u_{23} = ∣ 1.46489 \dots - 1.53343 \dots ∣ = 0.06854 \dots

Δ u_{23} = 0.06854 \dots

u_{24} = 1.39856 \dots : Δ u_{24} = 0.06633 \dots

f (u_{23}) = - 2 \cdot 1.46489 \dots^{24} - 0.44920 \dots \cdot 1.46489 \dots^{23} - 1.71281 \dots \cdot 1.46489 \dots^{22} - 0.74673 \dots \cdot 1.46489 \dots^{21} - 1.54817 \dots \cdot 1.46489 \dots^{20} - 0.94956 \dots \cdot 1.46489 \dots^{19} - 1.46104 \dots \cdot 1.46489 \dots^{18} - 1.09346 \dots \cdot 1.46489 \dots^{17} - 1.42313 \dots \cdot 1.46489 \dots^{16} - 1.20092 \dots \cdot 1.46489 \dots^{15} - 1.41671 \dots \cdot 1.46489 \dots^{14} - 1.28609 \dots \cdot 1.46489 \dots^{13} - 1.43067 \dots \cdot 1.46489 \dots^{12} - 1.35787 \dots \cdot 1.46489 \dots^{11} - 1.45804 \dots \cdot 1.46489 \dots^{10} - 1.42186 \dots \cdot 1.46489 \dots^{9} - 1.49448 \dots \cdot 1.46489 \dots^{8} - 1.48163 \dots \cdot 1.46489 \dots^{7} - 1.53726 \dots \cdot 1.46489 \dots^{6} - 1.53940 \dots \cdot 1.46489 \dots^{5} - 1.58472 \dots \cdot 1.46489 \dots^{4} - 1.59663 \dots \cdot 1.46489 \dots^{3} - 1.63583 \dots \cdot 1.46489 \dots^{2} + 0.34576 \dots \cdot 1.46489 \dots - 1.24075 \dots = - 40475.63043 \dots

f^{^{'}} (u_{23}) = - 48 \cdot 1.46489 \dots^{23} - 10.33165 \dots \cdot 1.46489 \dots^{22} - 37.68185 \dots \cdot 1.46489 \dots^{21} - 15.68150 \dots \cdot 1.46489 \dots^{20} - 30.96351 \dots \cdot 1.46489 \dots^{19} - 18.04170 \dots \cdot 1.46489 \dots^{18} - 26.29873 \dots \cdot 1.46489 \dots^{17} - 18.58884 \dots \cdot 1.46489 \dots^{16} - 22.77013 \dots \cdot 1.46489 \dots^{15} - 18.01385 \dots \cdot 1.46489 \dots^{14} - 19.83404 \dots \cdot 1.46489 \dots^{13} - 16.71920 \dots \cdot 1.46489 \dots^{12} - 17.16810 \dots \cdot 1.46489 \dots^{11} - 14.93657 \dots \cdot 1.46489 \dots^{10} - 14.58046 \dots \cdot 1.46489 \dots^{9} - 12.79681 \dots \cdot 1.46489 \dots^{8} - 11.95584 \dots \cdot 1.46489 \dots^{7} - 10.37141 \dots \cdot 1.46489 \dots^{6} - 9.22360 \dots \cdot 1.46489 \dots^{5} - 7.69703 \dots \cdot 1.46489 \dots^{4} - 6.33891 \dots \cdot 1.46489 \dots^{3} - 4.78989 \dots \cdot 1.46489 \dots^{2} - 3.27166 \dots \cdot 1.46489 \dots + 0.34576 \dots = - 610196.33667 \dots

u_{24} = 1.39856 \dots

Δ u_{24} = ∣ 1.39856 \dots - 1.46489 \dots ∣ = 0.06633 \dots

Δ u_{24} = 0.06633 \dots

u_{25} = 1.33413 \dots : Δ u_{25} = 0.06442 \dots

f (u_{24}) = - 2 \cdot 1.39856 \dots^{24} - 0.44920 \dots \cdot 1.39856 \dots^{23} - 1.71281 \dots \cdot 1.39856 \dots^{22} - 0.74673 \dots \cdot 1.39856 \dots^{21} - 1.54817 \dots \cdot 1.39856 \dots^{20} - 0.94956 \dots \cdot 1.39856 \dots^{19} - 1.46104 \dots \cdot 1.39856 \dots^{18} - 1.09346 \dots \cdot 1.39856 \dots^{17} - 1.42313 \dots \cdot 1.39856 \dots^{16} - 1.20092 \dots \cdot 1.39856 \dots^{15} - 1.41671 \dots \cdot 1.39856 \dots^{14} - 1.28609 \dots \cdot 1.39856 \dots^{13} - 1.43067 \dots \cdot 1.39856 \dots^{12} - 1.35787 \dots \cdot 1.39856 \dots^{11} - 1.45804 \dots \cdot 1.39856 \dots^{10} - 1.42186 \dots \cdot 1.39856 \dots^{9} - 1.49448 \dots \cdot 1.39856 \dots^{8} - 1.48163 \dots \cdot 1.39856 \dots^{7} - 1.53726 \dots \cdot 1.39856 \dots^{6} - 1.53940 \dots \cdot 1.39856 \dots^{5} - 1.58472 \dots \cdot 1.39856 \dots^{4} - 1.59663 \dots \cdot 1.39856 \dots^{3} - 1.63583 \dots \cdot 1.39856 \dots^{2} + 0.34576 \dots \cdot 1.39856 \dots - 1.24075 \dots = - 14668.17657 \dots

f^{^{'}} (u_{24}) = - 48 \cdot 1.39856 \dots^{23} - 10.33165 \dots \cdot 1.39856 \dots^{22} - 37.68185 \dots \cdot 1.39856 \dots^{21} - 15.68150 \dots \cdot 1.39856 \dots^{20} - 30.96351 \dots \cdot 1.39856 \dots^{19} - 18.04170 \dots \cdot 1.39856 \dots^{18} - 26.29873 \dots \cdot 1.39856 \dots^{17} - 18.58884 \dots \cdot 1.39856 \dots^{16} - 22.77013 \dots \cdot 1.39856 \dots^{15} - 18.01385 \dots \cdot 1.39856 \dots^{14} - 19.83404 \dots \cdot 1.39856 \dots^{13} - 16.71920 \dots \cdot 1.39856 \dots^{12} - 17.16810 \dots \cdot 1.39856 \dots^{11} - 14.93657 \dots \cdot 1.39856 \dots^{10} - 14.58046 \dots \cdot 1.39856 \dots^{9} - 12.79681 \dots \cdot 1.39856 \dots^{8} - 11.95584 \dots \cdot 1.39856 \dots^{7} - 10.37141 \dots \cdot 1.39856 \dots^{6} - 9.22360 \dots \cdot 1.39856 \dots^{5} - 7.69703 \dots \cdot 1.39856 \dots^{4} - 6.33891 \dots \cdot 1.39856 \dots^{3} - 4.78989 \dots \cdot 1.39856 \dots^{2} - 3.27166 \dots \cdot 1.39856 \dots + 0.34576 \dots = - 227676.73330 \dots

u_{25} = 1.33413 \dots

Δ u_{25} = ∣ 1.33413 \dots - 1.39856 \dots ∣ = 0.06442 \dots

Δ u_{25} = 0.06442 \dots

u_{26} = 1.27121 \dots : Δ u_{26} = 0.06292 \dots

f (u_{25}) = - 2 \cdot 1.33413 \dots^{24} - 0.44920 \dots \cdot 1.33413 \dots^{23} - 1.71281 \dots \cdot 1.33413 \dots^{22} - 0.74673 \dots \cdot 1.33413 \dots^{21} - 1.54817 \dots \cdot 1.33413 \dots^{20} - 0.94956 \dots \cdot 1.33413 \dots^{19} - 1.46104 \dots \cdot 1.33413 \dots^{18} - 1.09346 \dots \cdot 1.33413 \dots^{17} - 1.42313 \dots \cdot 1.33413 \dots^{16} - 1.20092 \dots \cdot 1.33413 \dots^{15} - 1.41671 \dots \cdot 1.33413 \dots^{14} - 1.28609 \dots \cdot 1.33413 \dots^{13} - 1.43067 \dots \cdot 1.33413 \dots^{12} - 1.35787 \dots \cdot 1.33413 \dots^{11} - 1.45804 \dots \cdot 1.33413 \dots^{10} - 1.42186 \dots \cdot 1.33413 \dots^{9} - 1.49448 \dots \cdot 1.33413 \dots^{8} - 1.48163 \dots \cdot 1.33413 \dots^{7} - 1.53726 \dots \cdot 1.33413 \dots^{6} - 1.53940 \dots \cdot 1.33413 \dots^{5} - 1.58472 \dots \cdot 1.33413 \dots^{4} - 1.59663 \dots \cdot 1.33413 \dots^{3} - 1.63583 \dots \cdot 1.33413 \dots^{2} + 0.34576 \dots \cdot 1.33413 \dots - 1.24075 \dots = - 5329.49040 \dots

f^{^{'}} (u_{25}) = - 48 \cdot 1.33413 \dots^{23} - 10.33165 \dots \cdot 1.33413 \dots^{22} - 37.68185 \dots \cdot 1.33413 \dots^{21} - 15.68150 \dots \cdot 1.33413 \dots^{20} - 30.96351 \dots \cdot 1.33413 \dots^{19} - 18.04170 \dots \cdot 1.33413 \dots^{18} - 26.29873 \dots \cdot 1.33413 \dots^{17} - 18.58884 \dots \cdot 1.33413 \dots^{16} - 22.77013 \dots \cdot 1.33413 \dots^{15} - 18.01385 \dots \cdot 1.33413 \dots^{14} - 19.83404 \dots \cdot 1.33413 \dots^{13} - 16.71920 \dots \cdot 1.33413 \dots^{12} - 17.16810 \dots \cdot 1.33413 \dots^{11} - 14.93657 \dots \cdot 1.33413 \dots^{10} - 14.58046 \dots \cdot 1.33413 \dots^{9} - 12.79681 \dots \cdot 1.33413 \dots^{8} - 11.95584 \dots \cdot 1.33413 \dots^{7} - 10.37141 \dots \cdot 1.33413 \dots^{6} - 9.22360 \dots \cdot 1.33413 \dots^{5} - 7.69703 \dots \cdot 1.33413 \dots^{4} - 6.33891 \dots \cdot 1.33413 \dots^{3} - 4.78989 \dots \cdot 1.33413 \dots^{2} - 3.27166 \dots \cdot 1.33413 \dots + 0.34576 \dots = - 84699.00020 \dots

u_{26} = 1.27121 \dots

Δ u_{26} = ∣ 1.27121 \dots - 1.33413 \dots ∣ = 0.06292 \dots

Δ u_{26} = 0.06292 \dots

u_{27} = 1.20920 \dots : Δ u_{27} = 0.06200 \dots

f (u_{26}) = - 2 \cdot 1.27121 \dots^{24} - 0.44920 \dots \cdot 1.27121 \dots^{23} - 1.71281 \dots \cdot 1.27121 \dots^{22} - 0.74673 \dots \cdot 1.27121 \dots^{21} - 1.54817 \dots \cdot 1.27121 \dots^{20} - 0.94956 \dots \cdot 1.27121 \dots^{19} - 1.46104 \dots \cdot 1.27121 \dots^{18} - 1.09346 \dots \cdot 1.27121 \dots^{17} - 1.42313 \dots \cdot 1.27121 \dots^{16} - 1.20092 \dots \cdot 1.27121 \dots^{15} - 1.41671 \dots \cdot 1.27121 \dots^{14} - 1.28609 \dots \cdot 1.27121 \dots^{13} - 1.43067 \dots \cdot 1.27121 \dots^{12} - 1.35787 \dots \cdot 1.27121 \dots^{11} - 1.45804 \dots \cdot 1.27121 \dots^{10} - 1.42186 \dots \cdot 1.27121 \dots^{9} - 1.49448 \dots \cdot 1.27121 \dots^{8} - 1.48163 \dots \cdot 1.27121 \dots^{7} - 1.53726 \dots \cdot 1.27121 \dots^{6} - 1.53940 \dots \cdot 1.27121 \dots^{5} - 1.58472 \dots \cdot 1.27121 \dots^{4} - 1.59663 \dots \cdot 1.27121 \dots^{3} - 1.63583 \dots \cdot 1.27121 \dots^{2} + 0.34576 \dots \cdot 1.27121 \dots - 1.24075 \dots = - 1944.44103 \dots

f^{^{'}} (u_{26}) = - 48 \cdot 1.27121 \dots^{23} - 10.33165 \dots \cdot 1.27121 \dots^{22} - 37.68185 \dots \cdot 1.27121 \dots^{21} - 15.68150 \dots \cdot 1.27121 \dots^{20} - 30.96351 \dots \cdot 1.27121 \dots^{19} - 18.04170 \dots \cdot 1.27121 \dots^{18} - 26.29873 \dots \cdot 1.27121 \dots^{17} - 18.58884 \dots \cdot 1.27121 \dots^{16} - 22.77013 \dots \cdot 1.27121 \dots^{15} - 18.01385 \dots \cdot 1.27121 \dots^{14} - 19.83404 \dots \cdot 1.27121 \dots^{13} - 16.71920 \dots \cdot 1.27121 \dots^{12} - 17.16810 \dots \cdot 1.27121 \dots^{11} - 14.93657 \dots \cdot 1.27121 \dots^{10} - 14.58046 \dots \cdot 1.27121 \dots^{9} - 12.79681 \dots \cdot 1.27121 \dots^{8} - 11.95584 \dots \cdot 1.27121 \dots^{7} - 10.37141 \dots \cdot 1.27121 \dots^{6} - 9.22360 \dots \cdot 1.27121 \dots^{5} - 7.69703 \dots \cdot 1.27121 \dots^{4} - 6.33891 \dots \cdot 1.27121 \dots^{3} - 4.78989 \dots \cdot 1.27121 \dots^{2} - 3.27166 \dots \cdot 1.27121 \dots + 0.34576 \dots = - 31357.58969 \dots

u_{27} = 1.20920 \dots

Δ u_{27} = ∣ 1.20920 \dots - 1.27121 \dots ∣ = 0.06200 \dots

Δ u_{27} = 0.06200 \dots

u_{28} = 1.14717 \dots : Δ u_{28} = 0.06203 \dots

f (u_{27}) = - 2 \cdot 1.20920 \dots^{24} - 0.44920 \dots \cdot 1.20920 \dots^{23} - 1.71281 \dots \cdot 1.20920 \dots^{22} - 0.74673 \dots \cdot 1.20920 \dots^{21} - 1.54817 \dots \cdot 1.20920 \dots^{20} - 0.94956 \dots \cdot 1.20920 \dots^{19} - 1.46104 \dots \cdot 1.20920 \dots^{18} - 1.09346 \dots \cdot 1.20920 \dots^{17} - 1.42313 \dots \cdot 1.20920 \dots^{16} - 1.20092 \dots \cdot 1.20920 \dots^{15} - 1.41671 \dots \cdot 1.20920 \dots^{14} - 1.28609 \dots \cdot 1.20920 \dots^{13} - 1.43067 \dots \cdot 1.20920 \dots^{12} - 1.35787 \dots \cdot 1.20920 \dots^{11} - 1.45804 \dots \cdot 1.20920 \dots^{10} - 1.42186 \dots \cdot 1.20920 \dots^{9} - 1.49448 \dots \cdot 1.20920 \dots^{8} - 1.48163 \dots \cdot 1.20920 \dots^{7} - 1.53726 \dots \cdot 1.20920 \dots^{6} - 1.53940 \dots \cdot 1.20920 \dots^{5} - 1.58472 \dots \cdot 1.20920 \dots^{4} - 1.59663 \dots \cdot 1.20920 \dots^{3} - 1.63583 \dots \cdot 1.20920 \dots^{2} + 0.34576 \dots \cdot 1.20920 \dots - 1.24075 \dots = - 714.29948 \dots

f^{^{'}} (u_{27}) = - 48 \cdot 1.20920 \dots^{23} - 10.33165 \dots \cdot 1.20920 \dots^{22} - 37.68185 \dots \cdot 1.20920 \dots^{21} - 15.68150 \dots \cdot 1.20920 \dots^{20} - 30.96351 \dots \cdot 1.20920 \dots^{19} - 18.04170 \dots \cdot 1.20920 \dots^{18} - 26.29873 \dots \cdot 1.20920 \dots^{17} - 18.58884 \dots \cdot 1.20920 \dots^{16} - 22.77013 \dots \cdot 1.20920 \dots^{15} - 18.01385 \dots \cdot 1.20920 \dots^{14} - 19.83404 \dots \cdot 1.20920 \dots^{13} - 16.71920 \dots \cdot 1.20920 \dots^{12} - 17.16810 \dots \cdot 1.20920 \dots^{11} - 14.93657 \dots \cdot 1.20920 \dots^{10} - 14.58046 \dots \cdot 1.20920 \dots^{9} - 12.79681 \dots \cdot 1.20920 \dots^{8} - 11.95584 \dots \cdot 1.20920 \dots^{7} - 10.37141 \dots \cdot 1.20920 \dots^{6} - 9.22360 \dots \cdot 1.20920 \dots^{5} - 7.69703 \dots \cdot 1.20920 \dots^{4} - 6.33891 \dots \cdot 1.20920 \dots^{3} - 4.78989 \dots \cdot 1.20920 \dots^{2} - 3.27166 \dots \cdot 1.20920 \dots + 0.34576 \dots = - 11515.29006 \dots

u_{28} = 1.14717 \dots

Δ u_{28} = ∣ 1.14717 \dots - 1.20920 \dots ∣ = 0.06203 \dots

Δ u_{28} = 0.06203 \dots

u_{29} = 1.08350 \dots : Δ u_{29} = 0.06367 \dots

f (u_{28}) = - 2 \cdot 1.14717 \dots^{24} - 0.44920 \dots \cdot 1.14717 \dots^{23} - 1.71281 \dots \cdot 1.14717 \dots^{22} - 0.74673 \dots \cdot 1.14717 \dots^{21} - 1.54817 \dots \cdot 1.14717 \dots^{20} - 0.94956 \dots \cdot 1.14717 \dots^{19} - 1.46104 \dots \cdot 1.14717 \dots^{18} - 1.09346 \dots \cdot 1.14717 \dots^{17} - 1.42313 \dots \cdot 1.14717 \dots^{16} - 1.20092 \dots \cdot 1.14717 \dots^{15} - 1.41671 \dots \cdot 1.14717 \dots^{14} - 1.28609 \dots \cdot 1.14717 \dots^{13} - 1.43067 \dots \cdot 1.14717 \dots^{12} - 1.35787 \dots \cdot 1.14717 \dots^{11} - 1.45804 \dots \cdot 1.14717 \dots^{10} - 1.42186 \dots \cdot 1.14717 \dots^{9} - 1.49448 \dots \cdot 1.14717 \dots^{8} - 1.48163 \dots \cdot 1.14717 \dots^{7} - 1.53726 \dots \cdot 1.14717 \dots^{6} - 1.53940 \dots \cdot 1.14717 \dots^{5} - 1.58472 \dots \cdot 1.14717 \dots^{4} - 1.59663 \dots \cdot 1.14717 \dots^{3} - 1.63583 \dots \cdot 1.14717 \dots^{2} + 0.34576 \dots \cdot 1.14717 \dots - 1.24075 \dots = - 265.47497 \dots

f^{^{'}} (u_{28}) = - 48 \cdot 1.14717 \dots^{23} - 10.33165 \dots \cdot 1.14717 \dots^{22} - 37.68185 \dots \cdot 1.14717 \dots^{21} - 15.68150 \dots \cdot 1.14717 \dots^{20} - 30.96351 \dots \cdot 1.14717 \dots^{19} - 18.04170 \dots \cdot 1.14717 \dots^{18} - 26.29873 \dots \cdot 1.14717 \dots^{17} - 18.58884 \dots \cdot 1.14717 \dots^{16} - 22.77013 \dots \cdot 1.14717 \dots^{15} - 18.01385 \dots \cdot 1.14717 \dots^{14} - 19.83404 \dots \cdot 1.14717 \dots^{13} - 16.71920 \dots \cdot 1.14717 \dots^{12} - 17.16810 \dots \cdot 1.14717 \dots^{11} - 14.93657 \dots \cdot 1.14717 \dots^{10} - 14.58046 \dots \cdot 1.14717 \dots^{9} - 12.79681 \dots \cdot 1.14717 \dots^{8} - 11.95584 \dots \cdot 1.14717 \dots^{7} - 10.37141 \dots \cdot 1.14717 \dots^{6} - 9.22360 \dots \cdot 1.14717 \dots^{5} - 7.69703 \dots \cdot 1.14717 \dots^{4} - 6.33891 \dots \cdot 1.14717 \dots^{3} - 4.78989 \dots \cdot 1.14717 \dots^{2} - 3.27166 \dots \cdot 1.14717 \dots + 0.34576 \dots = - 4169.45007 \dots

u_{29} = 1.08350 \dots

Δ u_{29} = ∣ 1.08350 \dots - 1.14717 \dots ∣ = 0.06367 \dots

Δ u_{29} = 0.06367 \dots

u_{30} = 1.01515 \dots : Δ u_{30} = 0.06834 \dots

f (u_{29}) = - 2 \cdot 1.08350 \dots^{24} - 0.44920 \dots \cdot 1.08350 \dots^{23} - 1.71281 \dots \cdot 1.08350 \dots^{22} - 0.74673 \dots \cdot 1.08350 \dots^{21} - 1.54817 \dots \cdot 1.08350 \dots^{20} - 0.94956 \dots \cdot 1.08350 \dots^{19} - 1.46104 \dots \cdot 1.08350 \dots^{18} - 1.09346 \dots \cdot 1.08350 \dots^{17} - 1.42313 \dots \cdot 1.08350 \dots^{16} - 1.20092 \dots \cdot 1.08350 \dots^{15} - 1.41671 \dots \cdot 1.08350 \dots^{14} - 1.28609 \dots \cdot 1.08350 \dots^{13} - 1.43067 \dots \cdot 1.08350 \dots^{12} - 1.35787 \dots \cdot 1.08350 \dots^{11} - 1.45804 \dots \cdot 1.08350 \dots^{10} - 1.42186 \dots \cdot 1.08350 \dots^{9} - 1.49448 \dots \cdot 1.08350 \dots^{8} - 1.48163 \dots \cdot 1.08350 \dots^{7} - 1.53726 \dots \cdot 1.08350 \dots^{6} - 1.53940 \dots \cdot 1.08350 \dots^{5} - 1.58472 \dots \cdot 1.08350 \dots^{4} - 1.59663 \dots \cdot 1.08350 \dots^{3} - 1.63583 \dots \cdot 1.08350 \dots^{2} + 0.34576 \dots \cdot 1.08350 \dots - 1.24075 \dots = - 100.65737 \dots

f^{^{'}} (u_{29}) = - 48 \cdot 1.08350 \dots^{23} - 10.33165 \dots \cdot 1.08350 \dots^{22} - 37.68185 \dots \cdot 1.08350 \dots^{21} - 15.68150 \dots \cdot 1.08350 \dots^{20} - 30.96351 \dots \cdot 1.08350 \dots^{19} - 18.04170 \dots \cdot 1.08350 \dots^{18} - 26.29873 \dots \cdot 1.08350 \dots^{17} - 18.58884 \dots \cdot 1.08350 \dots^{16} - 22.77013 \dots \cdot 1.08350 \dots^{15} - 18.01385 \dots \cdot 1.08350 \dots^{14} - 19.83404 \dots \cdot 1.08350 \dots^{13} - 16.71920 \dots \cdot 1.08350 \dots^{12} - 17.16810 \dots \cdot 1.08350 \dots^{11} - 14.93657 \dots \cdot 1.08350 \dots^{10} - 14.58046 \dots \cdot 1.08350 \dots^{9} - 12.79681 \dots \cdot 1.08350 \dots^{8} - 11.95584 \dots \cdot 1.08350 \dots^{7} - 10.37141 \dots \cdot 1.08350 \dots^{6} - 9.22360 \dots \cdot 1.08350 \dots^{5} - 7.69703 \dots \cdot 1.08350 \dots^{4} - 6.33891 \dots \cdot 1.08350 \dots^{3} - 4.78989 \dots \cdot 1.08350 \dots^{2} - 3.27166 \dots \cdot 1.08350 \dots + 0.34576 \dots = - 1472.71854 \dots

u_{30} = 1.01515 \dots

Δ u_{30} = ∣ 1.01515 \dots - 1.08350 \dots ∣ = 0.06834 \dots

Δ u_{30} = 0.06834 \dots

u_{31} = 0.93599 \dots : Δ u_{31} = 0.07916 \dots

f (u_{30}) = - 2 \cdot 1.01515 \dots^{24} - 0.44920 \dots \cdot 1.01515 \dots^{23} - 1.71281 \dots \cdot 1.01515 \dots^{22} - 0.74673 \dots \cdot 1.01515 \dots^{21} - 1.54817 \dots \cdot 1.01515 \dots^{20} - 0.94956 \dots \cdot 1.01515 \dots^{19} - 1.46104 \dots \cdot 1.01515 \dots^{18} - 1.09346 \dots \cdot 1.01515 \dots^{17} - 1.42313 \dots \cdot 1.01515 \dots^{16} - 1.20092 \dots \cdot 1.01515 \dots^{15} - 1.41671 \dots \cdot 1.01515 \dots^{14} - 1.28609 \dots \cdot 1.01515 \dots^{13} - 1.43067 \dots \cdot 1.01515 \dots^{12} - 1.35787 \dots \cdot 1.01515 \dots^{11} - 1.45804 \dots \cdot 1.01515 \dots^{10} - 1.42186 \dots \cdot 1.01515 \dots^{9} - 1.49448 \dots \cdot 1.01515 \dots^{8} - 1.48163 \dots \cdot 1.01515 \dots^{7} - 1.53726 \dots \cdot 1.01515 \dots^{6} - 1.53940 \dots \cdot 1.01515 \dots^{5} - 1.58472 \dots \cdot 1.01515 \dots^{4} - 1.59663 \dots \cdot 1.01515 \dots^{3} - 1.63583 \dots \cdot 1.01515 \dots^{2} + 0.34576 \dots \cdot 1.01515 \dots - 1.24075 \dots = - 39.46520 \dots

f^{^{'}} (u_{30}) = - 48 \cdot 1.01515 \dots^{23} - 10.33165 \dots \cdot 1.01515 \dots^{22} - 37.68185 \dots \cdot 1.01515 \dots^{21} - 15.68150 \dots \cdot 1.01515 \dots^{20} - 30.96351 \dots \cdot 1.01515 \dots^{19} - 18.04170 \dots \cdot 1.01515 \dots^{18} - 26.29873 \dots \cdot 1.01515 \dots^{17} - 18.58884 \dots \cdot 1.01515 \dots^{16} - 22.77013 \dots \cdot 1.01515 \dots^{15} - 18.01385 \dots \cdot 1.01515 \dots^{14} - 19.83404 \dots \cdot 1.01515 \dots^{13} - 16.71920 \dots \cdot 1.01515 \dots^{12} - 17.16810 \dots \cdot 1.01515 \dots^{11} - 14.93657 \dots \cdot 1.01515 \dots^{10} - 14.58046 \dots \cdot 1.01515 \dots^{9} - 12.79681 \dots \cdot 1.01515 \dots^{8} - 11.95584 \dots \cdot 1.01515 \dots^{7} - 10.37141 \dots \cdot 1.01515 \dots^{6} - 9.22360 \dots \cdot 1.01515 \dots^{5} - 7.69703 \dots \cdot 1.01515 \dots^{4} - 6.33891 \dots \cdot 1.01515 \dots^{3} - 4.78989 \dots \cdot 1.01515 \dots^{2} - 3.27166 \dots \cdot 1.01515 \dots + 0.34576 \dots = - 498.51394 \dots

u_{31} = 0.93599 \dots

Δ u_{31} = ∣ 0.93599 \dots - 1.01515 \dots ∣ = 0.07916 \dots

Δ u_{31} = 0.07916 \dots

Cannot find solution

The solutions are

u \approx 1.01704 \dots, u \approx - 0.79244 \dots

u \approx 1.01704 \dots, u \approx - 0.79244 \dots

Verify Solutions

Find undefined (singularity) points:

u = 0

Take the denominator(s) of

- 2 + \frac{1}{u ^{26}} + \frac{2}{u ^{23}}

and compare to zero

Solve

u^{26} = 0 : u = 0

u^{26} = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

u = 0

Solve

u^{23} = 0 : u = 0

u^{23} = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

u = 0

The following points are undefined

u = 0

Combine undefined points with solutions:

u \approx 1.01704 \dots, u \approx - 0.79244 \dots

Substitute back

u = csc (x)

csc (x) \approx 1.01704 \dots, csc (x) \approx - 0.79244 \dots

csc (x) \approx 1.01704 \dots, csc (x) \approx - 0.79244 \dots

csc (x) = 1.01704 \dots : x = arccsc (1.01704 \dots) + 2 πn, x = π - arccsc (1.01704 \dots) + 2 πn

csc (x) = 1.01704 \dots

Apply trig inverse properties

csc (x) = 1.01704 \dots

General solutions for

csc (x) = 1.01704 \dots

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

x = arccsc (1.01704 \dots) + 2 πn, x = π - arccsc (1.01704 \dots) + 2 πn

x = arccsc (1.01704 \dots) + 2 πn, x = π - arccsc (1.01704 \dots) + 2 πn

csc (x) = - 0.79244 \dots :

No Solution

csc (x) = - 0.79244 \dots

csc (x) \leq - 1 or csc (x) \geq 1

No Solution

Combine all the solutions

x = arccsc (1.01704 \dots) + 2 πn, x = π - arccsc (1.01704 \dots) + 2 πn

Show solutions in decimal form

x = 1.38743 \dots + 2 πn, x = π - 1.38743 \dots + 2 πn

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16^{sin(x)}=8^{csc(x)}

1 6^{s i n (x)} = 8^{c s c (x)}

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Frequently Asked Questions (FAQ)

What is the general solution for 2sin^{23}(x)+sin^{26}(x)-2=0 ?
The general solution for 2sin^{23}(x)+sin^{26}(x)-2=0 is x=1.38743…+2pin,x=pi-1.38743…+2pin