x^6-14x^4+3x^2-42=0

Lösung

x^{6} - 14 x^{4} + 3 x^{2} - 42 = 0

x = 14, x = - 14, x = \frac{4 3}{2} + \frac{4 3}{2} i, x = - \frac{4 3}{2} - \frac{4 3}{2} i, x = \frac{4 3}{2} - \frac{4 3}{2} i, x = - \frac{4 3}{2} + \frac{4 3}{2} i

Schritte zur Lösung

x^{6} - 14 x^{4} + 3 x^{2} - 42 = 0

Schreibe die Gleichung um mit

u = x^{2}, u^{2} = x^{4}

und

u^{3} = x^{6}

u^{3} - 14 u^{2} + 3 u - 42 = 0

Löse

u^{3} - 14 u^{2} + 3 u - 42 = 0 : u = 14, u = 3 i, u = - 3 i

u = 14, u = 3 i, u = - 3 i

Setze

u = x^{2} w i e d er e in,

löse für

x

Löse

x^{2} = 14 : x = 14, x = - 14

Löse

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

Löse

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

Die Lösungen sind

x = 14, x = - 14, x = \frac{4 3}{2} + \frac{4 3}{2} i, x = - \frac{4 3}{2} - \frac{4 3}{2} i, x = \frac{4 3}{2} - \frac{4 3}{2} i, x = - \frac{4 3}{2} + \frac{4 3}{2} i

x^{4} - x^{3} - 13 x^{2} + x + 12 = 0

s^{3} + 10.6 s^{2} + 7 s + 10 = 0

200 x - 0.02 x^{2} - 0.000002 x^{3} - 80000 = 0

2 x^{3} - 14 x^{2} + 2 x - 14 = 0

24 x^{3} + 46 x^{2} + 9 x - 9 = 0