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Beliebt Algebra >

x^8=16

Lösung

x^{8} = 16

Lösung

x = 2, x = - 2, x = 2 i, x = - 2 i, x = 1 + i, x = - 1 - i, x = 1 - i, x = - 1 + i

Schritte zur Lösung

x^{8} = 16

Schreibe die Gleichung um mit

u = x^{2}

und

u^{4} = x^{8}

u^{4} = 16

Löse

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

u = 2, u = - 2, u = 2 i, u = - 2 i

Setze

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

löse für

x

Löse

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

Löse

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

Löse

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

Löse

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

Die Lösungen sind

x = 2, x = - 2, x = 2 i, x = - 2 i, x = 1 + i, x = - 1 - i, x = 1 - i, x = - 1 + i

Graph

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