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Beliebt Algebra >

x^8-4x^6+4x^4-1=0

Lösung

x^{8} - 4 x^{6} + 4 x^{4} - 1 = 0

Lösung

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

Schritte zur Lösung

x^{8} - 4 x^{6} + 4 x^{4} - 1 = 0

Schreibe die Gleichung um mit

u = x^{2}, u^{2} = x^{4}, u^{3} = x^{6}

und

u^{4} = x^{8}

u^{4} - 4 u^{3} + 4 u^{2} - 1 = 0

Löse

u^{4} - 4 u^{3} + 4 u^{2} - 1 = 0 : u = 1, u = 1 + 2, u = 1 - 2

u = 1, u = 1 + 2, u = 1 - 2

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} = 1 + 2 : x = 1 + 2, x = - 1 + 2

Löse

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

Die Lösungen sind

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

Graph

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h^{3} = 1

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