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Beliebt Algebra >

x^{17}=x

Lösung

x^{17} = x

Lösung

x = 0, x = \frac{- 1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = - \frac{- 1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = \frac{- 1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = - \frac{- 1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = \frac{1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = \frac{1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{2}{2} + i \frac{2}{2}, x = - \frac{2}{2} - i \frac{2}{2}, x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2}{2} - i \frac{2}{2}, x = i, x = - i, x = - 1, x = 1

Schritte zur Lösung

x^{17} = x

Verschiebe

x

auf die linke Seite

x^{17} - x = 0

Faktorisiere

x^{17} - x : x (x^{4} + 2 x^{2} + 1) (x^{4} - 2 x^{2} + 1) (x^{2} + 2 x + 1) (x^{2} - 2 x + 1) (x^{2} + 1) (x + 1) (x - 1)

x (x^{4} + 2 x^{2} + 1) (x^{4} - 2 x^{2} + 1) (x^{2} + 2 x + 1) (x^{2} - 2 x + 1) (x^{2} + 1) (x + 1) (x - 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x^{4} + 2 x^{2} + 1 = 0 or x^{4} - 2 x^{2} + 1 = 0 or x^{2} + 2 x + 1 = 0 or x^{2} - 2 x + 1 = 0 or x^{2} + 1 = 0 or x + 1 = 0 or x - 1 = 0

Löse

x^{4} + 2 x^{2} + 1 = 0 : x = \frac{- 1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = - \frac{- 1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = \frac{- 1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = - \frac{- 1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i

Löse

x^{4} - 2 x^{2} + 1 = 0 : x = \frac{1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = \frac{1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i

Löse

x^{2} + 2 x + 1 = 0 : x = - \frac{2}{2} + i \frac{2}{2}, x = - \frac{2}{2} - i \frac{2}{2}

Löse

x^{2} - 2 x + 1 = 0 : x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2}{2} - i \frac{2}{2}

Löse

x^{2} + 1 = 0 : x = i, x = - i

Löse

x + 1 = 0 : x = - 1

Löse

x - 1 = 0 : x = 1

Die Lösungen sind

x = 0, x = \frac{- 1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = - \frac{- 1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = \frac{- 1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = - \frac{- 1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = \frac{1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = \frac{1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{2}{2} + i \frac{2}{2}, x = - \frac{2}{2} - i \frac{2}{2}, x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2}{2} - i \frac{2}{2}, x = i, x = - i, x = - 1, x = 1

Graph

Beliebte Beispiele

solvefor x,x^4+y^2+x^2y^2+16x^2-10x^2y=0

so l v e f or x, x^{4} + y^{2} + x^{2} y^{2} + 16 x^{2} - 10 x^{2} y = 0

solvefor x,x^3d^2-x^2d^1-3xy=x^2

so l v e f or x, x^{3} d^{2} - x^{2} d^{1} - 3 x y = x^{2}

x^{3} - 2 x^{2} = 75

x/3+3/9 =x^4+75

\frac{x}{3} + \frac{3}{9} = x^{4} + 75

- 3 x^{3} - 7 x + 6 = 0