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Beliebt Algebra >

x^6+7x^3-8=0

Lösung

x^{6} + 7 x^{3} - 8 = 0

Lösung

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

Schritte zur Lösung

x^{6} + 7 x^{3} - 8 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} + 7 u - 8 = 0

Löse

u^{2} + 7 u - 8 = 0 : u = 1, u = - 8

u = 1, u = - 8

Setze

u = x^{3} w i e d er e in,

löse für

x

Löse

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

Löse

x^{3} = - 8 : x = - 2, x = 1 - 3 i, x = 1 + 3 i

Die Lösungen sind

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

Graph

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