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Beliebt Algebra >

x^6+65x^3+64=0

Lösung

x^{6} + 65 x^{3} + 64 = 0

Lösung

x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i, x = - 4, x = 2 - 23 i, x = 2 + 23 i

Schritte zur Lösung

x^{6} + 65 x^{3} + 64 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} + 65 u + 64 = 0

Löse

u^{2} + 65 u + 64 = 0 : u = - 1, u = - 64

u = - 1, u = - 64

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} = - 64 : x = - 4, x = 2 - 23 i, x = 2 + 23 i

Die Lösungen sind

x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i, x = - 4, x = 2 - 23 i, x = 2 + 23 i

Graph

Beliebte Beispiele

2x^3-x^2-8x+4=0

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2 x^{3} + x^{2} + x - 1 = 0