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Beliebt Algebra >

8x^6+7x^3-1=0

Lösung

8 x^{6} + 7 x^{3} - 1 = 0

Lösung

x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i, x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i

Schritte zur Lösung

8 x^{6} + 7 x^{3} - 1 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

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

Löse

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

u = \frac{1}{8}, u = - 1

Setze

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

löse für

x

Löse

x^{3} = \frac{1}{8} : x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} 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 = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i, x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i

Graph

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