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Beliebt Algebra >

x^6= 1/729

Lösung

x^{6} = \frac{1}{729}

Lösung

x = \frac{1}{3}, x = - \frac{1}{3}, x = \frac{1}{6} + \frac{1}{2 3} i, x = - \frac{1}{6} - \frac{1}{2 3} i, x = \frac{1}{6} - \frac{1}{2 3} i, x = - \frac{1}{6} + \frac{1}{2 3} i

Schritte zur Lösung

x^{6} = \frac{1}{729}

Schreibe die Gleichung um mit

u = x^{2}

und

u^{3} = x^{6}

u^{3} = \frac{1}{729}

Löse

u^{3} = \frac{1}{729} : u = 3 \frac{1}{729}, u = 3 \frac{1}{729} \frac{- 1 + 3 i}{2}, u = 3 \frac{1}{729} \frac{- 1 - 3 i}{2}

u = 3 \frac{1}{729}, u = 3 \frac{1}{729} \frac{- 1 + 3 i}{2}, u = 3 \frac{1}{729} \frac{- 1 - 3 i}{2}

Setze

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

löse für

x

Löse

x^{2} = 3 \frac{1}{729} : x = \frac{1}{3}, x = - \frac{1}{3}

Löse

x^{2} = 3 \frac{1}{729} \frac{- 1 + 3 i}{2} : x = \frac{1}{6} + \frac{1}{2 3} i, x = - \frac{1}{6} - \frac{1}{2 3} i

Löse

x^{2} = 3 \frac{1}{729} \frac{- 1 - 3 i}{2} : x = \frac{1}{6} - \frac{1}{2 3} i, x = - \frac{1}{6} + \frac{1}{2 3} i

Die Lösungen sind

x = \frac{1}{3}, x = - \frac{1}{3}, x = \frac{1}{6} + \frac{1}{2 3} i, x = - \frac{1}{6} - \frac{1}{2 3} i, x = \frac{1}{6} - \frac{1}{2 3} i, x = - \frac{1}{6} + \frac{1}{2 3} i

Graph

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