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Beliebt Algebra >

27x^6+26x^3-1=0

Lösung

27 x^{6} + 26 x^{3} - 1 = 0

Lösung

x = \frac{1}{3}, x = - \frac{1}{6} + \frac{1}{2 3} i, x = - \frac{1}{6} - \frac{1}{2 3} i, x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i

Schritte zur Lösung

27 x^{6} + 26 x^{3} - 1 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

27 u^{2} + 26 u - 1 = 0

Löse

27 u^{2} + 26 u - 1 = 0 : u = \frac{1}{27}, u = - 1

u = \frac{1}{27}, u = - 1

Setze

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

löse für

x

Löse

x^{3} = \frac{1}{27} : x = \frac{1}{3}, x = - \frac{1}{6} + \frac{1}{2 3} i, x = - \frac{1}{6} - \frac{1}{2 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 = \frac{1}{3}, x = - \frac{1}{6} + \frac{1}{2 3} i, x = - \frac{1}{6} - \frac{1}{2 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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