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Beliebt Algebra >

x^4-2x^2+2=0

Lösung

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

Lösung

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

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 2 u + 2 = 0

Löse

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

u = 1 + i, u = 1 - i

Setze

u = x^{2} w i e d er e in,

löse für

x

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

8 y^{3} - 125 = 0

(x + 6)^{4} = 0

4 x^{3} - 6 x^{2} + 1 = 0

x^{4} - 5 x = 0

20u^4-13u^2+2=0

20 u^{4} - 13 u^{2} + 2 = 0