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Beliebt Algebra >

x^8+80x^4=81

Lösung

x^{8} + 80 x^{4} = 81

Lösung

x = 1, x = - 1, x = i, x = - i, x = \frac{3}{2} + \frac{3}{2} i, x = - \frac{3}{2} - \frac{3}{2} i, x = \frac{3}{2} - \frac{3}{2} i, x = - \frac{3}{2} + \frac{3}{2} i

Schritte zur Lösung

x^{8} + 80 x^{4} = 81

Verschiebe

81

auf die linke Seite

x^{8} + 80 x^{4} - 81 = 0

Schreibe die Gleichung um mit

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

und

u^{4} = x^{8}

u^{4} + 80 u^{2} - 81 = 0

Löse

u^{4} + 80 u^{2} - 81 = 0 : u = 1, u = - 1, u = 9 i, u = - 9 i

u = 1, u = - 1, u = 9 i, u = - 9 i

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 : x = i, x = - i

Löse

x^{2} = 9 i : x = \frac{3}{2} + \frac{3}{2} i, x = - \frac{3}{2} - \frac{3}{2} i

Löse

x^{2} = - 9 i : x = \frac{3}{2} - \frac{3}{2} i, x = - \frac{3}{2} + \frac{3}{2} i

Die Lösungen sind

x = 1, x = - 1, x = i, x = - i, x = \frac{3}{2} + \frac{3}{2} i, x = - \frac{3}{2} - \frac{3}{2} i, x = \frac{3}{2} - \frac{3}{2} i, x = - \frac{3}{2} + \frac{3}{2} i

Graph

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