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Beliebt Algebra >

x^8-15x^4-16=0

Lösung

x^{8} - 15 x^{4} - 16 = 0

Lösung

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

Schritte zur Lösung

x^{8} - 15 x^{4} - 16 = 0

Schreibe die Gleichung um mit

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

und

u^{4} = x^{8}

u^{4} - 15 u^{2} - 16 = 0

Löse

u^{4} - 15 u^{2} - 16 = 0 : u = 4, u = - 4, u = i, u = - i

u = 4, u = - 4, u = i, u = - i

Setze

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

löse für

x

Löse

x^{2} = 4 : x = 2, x = - 2

Löse

x^{2} = - 4 : x = 2 i, x = - 2 i

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

- 2 x^{4} + 7 = 2 x + 5

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

9 x^{6} = 36 x^{4}