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Beliebt Algebra >

solvefor x,fsif(x)=x^2-3x+2

Lösung

löse nach

x, f s i f (x) = x^{2} - 3 x + 2

Lösung

x = \frac{s ff ( x ) + 3 - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}{2 - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}} + - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8} i, x = - \frac{s ff ( x ) - 3 - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}{2 - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}} - - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8} i, x = \frac{s ff ( x ) + 3 - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}{2 - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}} + - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8} i, x = - \frac{s ff ( x ) - 3 - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}{2 - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}} - - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8} i

Schritte zur Lösung

f s i f (x) = x^{2} - 3 x + 2

Ersetze

x = a + bi

f s i f (x) = (a + bi)^{2} - 3 (a + bi) + 2

Schreibe

(a + bi)^{2} - 3 (a + bi) + 2

um:

(a^{2} - b^{2} - 3 a + 2) + i (- 3 b + 2 ab)

f s i f (x) = (a^{2} - b^{2} - 3 a + 2) + i (- 3 b + 2 ab)

Schreibe

f s i f (x)

in der Standard komplexen Form um:

0 + f s f (x) i

0 + f s f (x) i = (a^{2} - b^{2} - 3 a + 2) + i (- 3 b + 2 ab)

Komplexe Zahlen können nur gleich sein wenn ihre realen und imaginären Teile gleich sind.Schreibe als Gleichungssystem um

[0 = a^{2} - b^{2} - 3 a + 2 f s f (x) = - 3 b + 2 ab]

[0 = a^{2} - b^{2} - 3 a + 2 f s f (x) = - 3 b + 2 ab] : a = \frac{s ff ( x ) + 3 - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}{2 - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}, a = - \frac{s ff ( x ) - 3 - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}{2 - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}, a = \frac{s ff ( x ) + 3 - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}{2 - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}, a = - \frac{s ff ( x ) - 3 - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}{2 - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}, b = - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8} b = - - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8} b = - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8} b = - - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}

Setze in

x = a + bi

ein

x = \frac{s ff ( x ) + 3 - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}{2 - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}} + - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8} i, x = - \frac{s ff ( x ) - 3 - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}{2 - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}} - - \frac{1 + 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8} i, x = \frac{s ff ( x ) + 3 - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}{2 - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}} + - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8} i, x = - \frac{s ff ( x ) - 3 - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}}{2 - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8}} - - \frac{1 - 1 + 16 s ^{2} f ^{2} f ( x ) ^{2}}{8} i

Beliebte Beispiele

x^{2} + 2 - i = 0

x + y i - x i + y = 3

y+1= 4/3 (x-3)ina

y + 1 = \frac{4}{3} (x - 3) ina

x + y i = 8 - 5

4x+i(3x-y)=3-i^6

4 x + i (3 x - y) = 3 - i^{6}