x^4-2x^2+8=0

Lösung

x^{4} - 2 x^{2} + 8 = 0

x = \frac{1 + 2 2}{2} + \frac{7}{2 1 + 2 2} i, x = - \frac{1 + 2 2}{2} - \frac{7}{2 1 + 2 2} i, x = \frac{1 + 2 2}{2} - \frac{7}{2 1 + 2 2} i, x = - \frac{1 + 2 2}{2} + \frac{7}{2 1 + 2 2} i

Schritte zur Lösung

x^{4} - 2 x^{2} + 8 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

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

Löse

u^{2} - 2 u + 8 = 0 : u = 1 + 7 i, u = 1 - 7 i

u = 1 + 7 i, u = 1 - 7 i

Setze

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

löse für

x

Löse

x^{2} = 1 + 7 i : x = \frac{1 + 2 2}{2} + \frac{7}{2 1 + 2 2} i, x = - \frac{1 + 2 2}{2} - \frac{7}{2 1 + 2 2} i

Löse

x^{2} = 1 - 7 i : x = \frac{1 + 2 2}{2} - \frac{7}{2 1 + 2 2} i, x = - \frac{1 + 2 2}{2} + \frac{7}{2 1 + 2 2} i

Die Lösungen sind

x = \frac{1 + 2 2}{2} + \frac{7}{2 1 + 2 2} i, x = - \frac{1 + 2 2}{2} - \frac{7}{2 1 + 2 2} i, x = \frac{1 + 2 2}{2} - \frac{7}{2 1 + 2 2} i, x = - \frac{1 + 2 2}{2} + \frac{7}{2 1 + 2 2} i

627 x^{59} x a = 487 x^{36} x b

roo t s x^{3} + 3 x^{2} - 4 x - 12 = 0

x^{3} - \frac{5}{6} x^{2} + \frac{35}{6} x + 1 = 0

z^{12} = 1

x^{3} - 14 x^{2} + 12 x + 12 = 0