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Beliebt Algebra >

x^8+16=17x^4

Lösung

x^{8} + 16 = 17 x^{4}

Lösung

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

Schritte zur Lösung

x^{8} + 16 = 17 x^{4}

Verschiebe

17 x^{4}

auf die linke Seite

x^{8} + 16 - 17 x^{4} = 0

Schreibe in der Standard Form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{8} - 17 x^{4} + 16 = 0

Schreibe die Gleichung um mit

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

und

u^{4} = x^{8}

u^{4} - 17 u^{2} + 16 = 0

Löse

u^{4} - 17 u^{2} + 16 = 0 : u = 4, u = - 4, u = 1, u = - 1

u = 4, u = - 4, u = 1, u = - 1

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} = 1 : x = 1, x = - 1

Löse

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

Die Lösungen sind

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

Graph

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