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Beliebt Algebra >

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

Lösung

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

Lösung

x = 2, x = - 1 + 3 i, x = - 1 - 3 i, x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} 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 = 8, u = - 1

u = 8, u = - 1

Setze

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

löse für

x

Löse

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

Löse

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

Die Lösungen sind

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

Graph

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