2x^4-5x^2-3=0

Lösung

2 x^{4} - 5 x^{2} - 3 = 0

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

Schritte zur Lösung

2 x^{4} - 5 x^{2} - 3 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

2 u^{2} - 5 u - 3 = 0

Löse

2 u^{2} - 5 u - 3 = 0 : u = 3, u = - \frac{1}{2}

u = 3, u = - \frac{1}{2}

Setze

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

löse für

x

Löse

x^{2} = 3 : x = 3, x = - 3

Löse

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

Die Lösungen sind

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

x^{4} + 4 x^{3} + 5 x^{2} + 4 x + 1 = 0

r a t i o na l roo t s t es t 5 x^{3} + 27 x^{2} - 11 x + 5

x^{5} - x^{4} - x^{3} + x^{2} - 2 x + 2 = 0

so l v e f or y, 4 x^{3} - 16 y = 4 y^{3} - 16 x

4 x^{7} - 64 x^{3} = 0