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Beliebt Algebra >

(x^3-6)^2+3(x^3-6)-10=0

Lösung

(x^{3} - 6)^{2} + 3 (x^{3} - 6) - 10 = 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^{3} - 6)^{2} + 3 (x^{3} - 6) - 10 = 0

Schreibe

(x^{3} - 6)^{2} + 3 (x^{3} - 6) - 10

um:

x^{6} - 9 x^{3} + 8

x^{6} - 9 x^{3} + 8 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} - 9 u + 8 = 0

Löse

u^{2} - 9 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

Beliebte Beispiele

3 c^{3} + 9 = - 72

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x^3+4x^2-36x-144=0

x^{3} + 4 x^{2} - 36 x - 144 = 0

x^{3} - 9 x^{2} - 4 = 0