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Beliebt Algebra >

x^4=-81

Lösung

x^{4} = - 81

Lösung

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

Schritte zur Lösung

x^{4} = - 81

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} = - 81

Löse

u^{2} = - 81 : u = 9 i, u = - 9 i

u = 9 i, u = - 9 i

Setze

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

löse für

x

Löse

x^{2} = 9 i : x = \frac{3}{2} + \frac{3}{2} i, x = - \frac{3}{2} - \frac{3}{2} i

Löse

x^{2} = - 9 i : x = \frac{3}{2} - \frac{3}{2} i, x = - \frac{3}{2} + \frac{3}{2} i

Die Lösungen sind

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

Graph

Beliebte Beispiele

x^{4} - 4 x - 1 = 0

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

x^{3} + 5 x^{2} + 2 x = 0

x (x + 4) (4 x - 3) = 0

16 x^{4} + 25 = 41 x^{2}