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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

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

Löse

u^{2} - 2 u + 4 = 0 : u = 1 + 3 i, u = 1 - 3 i

u = 1 + 3 i, u = 1 - 3 i

Setze

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

löse für

x

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

r^{3} - 3 r^{2} - r + 3 = 0

x^4-17/4 x^2+1=0

x^{4} - \frac{17}{4} x^{2} + 1 = 0

x^{3} + 6 x + 12 = 0

- 49 x^{4} + 9 x^{2} = 0

t^3-9t^2+24t-8=0

t^{3} - 9 t^{2} + 24 t - 8 = 0