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Beliebt Algebra >

x^6-x^4+5x^2-5=0

Lösung

x^{6} - x^{4} + 5 x^{2} - 5 = 0

Lösung

x = 1, x = - 1, x = \frac{4 5}{2} + \frac{4 5}{2} i, x = - \frac{4 5}{2} - \frac{4 5}{2} i, x = \frac{4 5}{2} - \frac{4 5}{2} i, x = - \frac{4 5}{2} + \frac{4 5}{2} i

Schritte zur Lösung

x^{6} - x^{4} + 5 x^{2} - 5 = 0

Schreibe die Gleichung um mit

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

und

u^{3} = x^{6}

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

Löse

u^{3} - u^{2} + 5 u - 5 = 0 : u = 1, u = 5 i, u = - 5 i

u = 1, u = 5 i, u = - 5 i

Setze

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

löse für

x

Löse

x^{2} = 1 : x = 1, x = - 1

Löse

x^{2} = 5 i : x = \frac{4 5}{2} + \frac{4 5}{2} i, x = - \frac{4 5}{2} - \frac{4 5}{2} i

Löse

x^{2} = - 5 i : x = \frac{4 5}{2} - \frac{4 5}{2} i, x = - \frac{4 5}{2} + \frac{4 5}{2} i

Die Lösungen sind

x = 1, x = - 1, x = \frac{4 5}{2} + \frac{4 5}{2} i, x = - \frac{4 5}{2} - \frac{4 5}{2} i, x = \frac{4 5}{2} - \frac{4 5}{2} i, x = - \frac{4 5}{2} + \frac{4 5}{2} i

Graph

Beliebte Beispiele

5 w^{3} = 50 w

24 x^{2} + 4 x^{3} = 0

5 x^{4} - 6 x^{2} = 0

4 x^{3} - 18 x^{2} = 0

2 y^{3} + 6 y = 1