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Beliebt Algebra >

x^8-8=0

Lösung

x^{8} - 8 = 0

Lösung

x = 48, x = - 48, x = 48 i, x = - 48 i, x = \frac{1}{4 2} + \frac{1}{8 2} i, x = - \frac{1}{4 2} - \frac{1}{8 2} i, x = \frac{1}{4 2} - \frac{1}{8 2} i, x = - \frac{1}{4 2} + \frac{1}{8 2} i

Schritte zur Lösung

x^{8} - 8 = 0

Verschiebe

8

auf die rechte Seite

x^{8} = 8

Schreibe die Gleichung um mit

u = x^{2}

und

u^{4} = x^{8}

u^{4} = 8

Löse

u^{4} = 8 : u = 4 2^{3}, u = - 4 2^{3}, u = 4 2^{3} i, u = - 4 2^{3} i

u = 4 2^{3}, u = - 4 2^{3}, u = 4 2^{3} i, u = - 4 2^{3} i

Setze

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

löse für

x

Löse

x^{2} = 4 2^{3} : x = 48, x = - 48

Löse

x^{2} = - 4 2^{3} : x = 48 i, x = - 48 i

Löse

x^{2} = 4 2^{3} i : x = \frac{1}{4 2} + \frac{1}{8 2} i, x = - \frac{1}{4 2} - \frac{1}{8 2} i

Löse

x^{2} = - 4 2^{3} i : x = \frac{1}{4 2} - \frac{1}{8 2} i, x = - \frac{1}{4 2} + \frac{1}{8 2} i

Die Lösungen sind

x = 48, x = - 48, x = 48 i, x = - 48 i, x = \frac{1}{4 2} + \frac{1}{8 2} i, x = - \frac{1}{4 2} - \frac{1}{8 2} i, x = \frac{1}{4 2} - \frac{1}{8 2} i, x = - \frac{1}{4 2} + \frac{1}{8 2} i

Graph

Beliebte Beispiele

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

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

g^{3} = 8

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x (x - 1) (x + 3) = 0