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Beliebt Algebra >

x^6+6x^3-7=0

Lösung

x^{6} + 6 x^{3} - 7 = 0

Lösung

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = - 37, x = - \frac{3 7 ( - 1 + 3 i )}{2}, x = - \frac{3 7 ( - 1 - 3 i )}{2}

Schritte zur Lösung

x^{6} + 6 x^{3} - 7 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} + 6 u - 7 = 0

Löse

u^{2} + 6 u - 7 = 0 : u = 1, u = - 7

u = 1, u = - 7

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} = - 7 : x = - 37, x = - \frac{3 7 ( - 1 + 3 i )}{2}, x = - \frac{3 7 ( - 1 - 3 i )}{2}

Die Lösungen sind

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = - 37, x = - \frac{3 7 ( - 1 + 3 i )}{2}, x = - \frac{3 7 ( - 1 - 3 i )}{2}

Graph

Beliebte Beispiele

2 x^{3} - 11 x = - 9

(4x^3+12x^2-1)=0

(4 x^{3} + 12 x^{2} - 1) = 0

a^6=16a^{20},a^4=10

a^{6} = 16 a^{20}, a^{4} = 10

-4x^3+16x^2-9x-9=0

- 4 x^{3} + 16 x^{2} - 9 x - 9 = 0

x^{4} + x^{2} = 6