x^4= 1/81

Lösung

x^{4} = \frac{1}{81}

x = \frac{1}{3}, x = - \frac{1}{3}, x = \frac{1}{3} i, x = - \frac{1}{3} i

Schritte zur Lösung

x^{4} = \frac{1}{81}

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} = \frac{1}{81}

Löse

u^{2} = \frac{1}{81} : u = \frac{1}{81}, u = - \frac{1}{81}

u = \frac{1}{81}, u = - \frac{1}{81}

Setze

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

löse für

x

Löse

x^{2} = \frac{1}{81} : x = \frac{1}{3}, x = - \frac{1}{3}

Löse

x^{2} = - \frac{1}{81} : x = \frac{1}{3} i, x = - \frac{1}{3} i

Die Lösungen sind

x = \frac{1}{3}, x = - \frac{1}{3}, x = \frac{1}{3} i, x = - \frac{1}{3} i

x^{3} + 2 x^{2} - 5 x - 10 = 0

roo t s x^{4} - 5 x^{2} + 4 = 0

2 x^{3} + 2 x^{2} + 1 = 0

12 x - 6 x^{2} + 3 x^{4} = 6 x^{3} + 2 x - x^{4}

4 x^{3} + 56 x^{2} + 132 x = 0