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Beliebt Algebra >

6x^4=-16,x^4=1

Lösung

6 x^{4} = - 16, x^{4} = 1

Lösung

x = 4 \frac{2}{3} + \frac{2}{3 4 \frac{2}{3}} i, x = - 4 \frac{2}{3} - \frac{2}{3 4 \frac{2}{3}} i, x = 4 \frac{2}{3} - \frac{2}{3 4 \frac{2}{3}} i, x = - 4 \frac{2}{3} + \frac{2}{3 4 \frac{2}{3}} i

Schritte zur Lösung

6 x^{4} = - 16, x^{4} = 1

Teile beide Seiten durch

6

x^{4} = - \frac{8}{3}

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} = - \frac{8}{3}

Löse

u^{2} = - \frac{8}{3} : u = \frac{2 2}{3} i, u = - \frac{2 2}{3} i

u = \frac{2 2}{3} i, u = - \frac{2 2}{3} i

Setze

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

löse für

x

Löse

x^{2} = \frac{2 2}{3} i : x = 4 \frac{2}{3} + \frac{2}{3 4 \frac{2}{3}} i, x = - 4 \frac{2}{3} - \frac{2}{3 4 \frac{2}{3}} i

Löse

x^{2} = - \frac{2 2}{3} i : x = 4 \frac{2}{3} - \frac{2}{3 4 \frac{2}{3}} i, x = - 4 \frac{2}{3} + \frac{2}{3 4 \frac{2}{3}} i

Die Lösungen sind

x = 4 \frac{2}{3} + \frac{2}{3 4 \frac{2}{3}} i, x = - 4 \frac{2}{3} - \frac{2}{3 4 \frac{2}{3}} i, x = 4 \frac{2}{3} - \frac{2}{3 4 \frac{2}{3}} i, x = - 4 \frac{2}{3} + \frac{2}{3 4 \frac{2}{3}} i

Graph

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