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Beliebt Algebra >

x^8-9x^4+8=0

Lösung

x^{8} - 9 x^{4} + 8 = 0

Lösung

x = 4 2^{3}, x = - 4 2^{3}, x = 4 2^{3} i, x = - 4 2^{3} i, x = 1, x = - 1, x = i, x = - i

Schritte zur Lösung

x^{8} - 9 x^{4} + 8 = 0

Schreibe die Gleichung um mit

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

und

u^{4} = x^{8}

u^{4} - 9 u^{2} + 8 = 0

Löse

u^{4} - 9 u^{2} + 8 = 0 : u = 22, u = - 22, u = 1, u = - 1

u = 22, u = - 22, u = 1, u = - 1

Setze

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

löse für

x

Löse

x^{2} = 22 : x = 4 2^{3}, x = - 4 2^{3}

Löse

x^{2} = - 22 : x = 4 2^{3} i, x = - 4 2^{3} i

Löse

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

Löse

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

Die Lösungen sind

x = 4 2^{3}, x = - 4 2^{3}, x = 4 2^{3} i, x = - 4 2^{3} i, x = 1, x = - 1, x = i, x = - i

Graph

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