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Beliebt Algebra >

x^6-2=0

Lösung

x^{6} - 2 = 0

Lösung

x = 32, x = - 32, x = \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i

Schritte zur Lösung

x^{6} - 2 = 0

Verschiebe

2

auf die rechte Seite

x^{6} = 2

Schreibe die Gleichung um mit

u = x^{2}

und

u^{3} = x^{6}

u^{3} = 2

Löse

u^{3} = 2 : u = 32, u = 32 \frac{- 1 + 3 i}{2}, u = 32 \frac{- 1 - 3 i}{2}

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

Setze

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

löse für

x

Löse

x^{2} = 32 : x = 32, x = - 32

Löse

x^{2} = 32 \frac{- 1 + 3 i}{2} : x = \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i

Löse

x^{2} = 32 \frac{- 1 - 3 i}{2} : x = \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i

Die Lösungen sind

x = 32, x = - 32, x = \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i

Graph

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