x^6+126x^3+125=0

Lösung

x^{6} + 126 x^{3} + 125 = 0

x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i, x = - 5, x = \frac{5}{2} - \frac{5 3}{2} i, x = \frac{5}{2} + \frac{5 3}{2} i

Schritte zur Lösung

x^{6} + 126 x^{3} + 125 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} + 126 u + 125 = 0

Löse

u^{2} + 126 u + 125 = 0 : u = - 1, u = - 125

u = - 1, u = - 125

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} = - 125 : x = - 5, x = \frac{5}{2} - \frac{5 3}{2} i, x = \frac{5}{2} + \frac{5 3}{2} i

Die Lösungen sind

x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i, x = - 5, x = \frac{5}{2} - \frac{5 3}{2} i, x = \frac{5}{2} + \frac{5 3}{2} i

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

f a c t or x^{8} - 17 x^{4} + 16 = 0

72 x^{7} - 504 x^{6} = 0

x + 3 = x^{3} + 10 x^{2} + 28 x + 21

2 x^{4} + 9 x^{3} + 15 x^{2} + 11 x + 3 = 0