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Beliebt Algebra >

x^6-28x^3+27=0

Lösung

x^{6} - 28 x^{3} + 27 = 0

Lösung

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

Schritte zur Lösung

x^{6} - 28 x^{3} + 27 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} - 28 u + 27 = 0

Löse

u^{2} - 28 u + 27 = 0 : u = 27, u = 1

u = 27, u = 1

Setze

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

löse für

x

Löse

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

Graph

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x^6-124x^3-125=0

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