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Beliebt Algebra >

x^6+x^3-2=0

Lösung

x^{6} + x^{3} - 2 = 0

Lösung

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = - 32, x = \frac{3 2}{2} - i \frac{3 2 3}{2}, x = \frac{3 2}{2} + i \frac{3 2 3}{2}

Schritte zur Lösung

x^{6} + x^{3} - 2 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} + u - 2 = 0

Löse

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

u = 1, u = - 2

Setze

u = x^{3} w i e d er e in,

löse für

x

Löse

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

Löse

x^{3} = - 2 : x = - 32, x = \frac{3 2}{2} - i \frac{3 2 3}{2}, x = \frac{3 2}{2} + i \frac{3 2 3}{2}

Die Lösungen sind

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = - 32, x = \frac{3 2}{2} - i \frac{3 2 3}{2}, x = \frac{3 2}{2} + i \frac{3 2 3}{2}

Graph

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