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Beliebt Algebra >

x^6+12x^3+32=0

Lösung

x^{6} + 12 x^{3} + 32 = 0

Lösung

x = - 34, x = \frac{1}{3 2} - \frac{3}{3 2} i, x = \frac{1}{3 2} + \frac{3}{3 2} i, x = - 2, x = 1 - 3 i, x = 1 + 3 i

Schritte zur Lösung

x^{6} + 12 x^{3} + 32 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} + 12 u + 32 = 0

Löse

u^{2} + 12 u + 32 = 0 : u = - 4, u = - 8

u = - 4, u = - 8

Setze

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

löse für

x

Löse

x^{3} = - 4 : x = - 34, x = \frac{1}{3 2} - \frac{3}{3 2} i, x = \frac{1}{3 2} + \frac{3}{3 2} i

Löse

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

Die Lösungen sind

x = - 34, x = \frac{1}{3 2} - \frac{3}{3 2} i, x = \frac{1}{3 2} + \frac{3}{3 2} i, x = - 2, x = 1 - 3 i, x = 1 + 3 i

Graph

Beliebte Beispiele

solvefor x,y^2=cx^4-2

so l v e f or x, y^{2} = c x^{4} - 2

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(x + 3) (x^{2} + 3 x + 5) = x^{2} + 3 x

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

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