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Beliebt Algebra >

b^6=7

Lösung

b^{6} = 7

Lösung

b = 37, b = - 37, b = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i

Schritte zur Lösung

b^{6} = 7

Schreibe die Gleichung um mit

u = b^{2}

und

u^{3} = b^{6}

u^{3} = 7

Löse

u^{3} = 7 : u = 37, u = 37 \frac{- 1 + 3 i}{2}, u = 37 \frac{- 1 - 3 i}{2}

u = 37, u = 37 \frac{- 1 + 3 i}{2}, u = 37 \frac{- 1 - 3 i}{2}

Setze

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

löse für

b

Löse

b^{2} = 37 : b = 37, b = - 37

Löse

b^{2} = 37 \frac{- 1 + 3 i}{2} : b = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i

Löse

b^{2} = 37 \frac{- 1 - 3 i}{2} : b = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i

Die Lösungen sind

b = 37, b = - 37, b = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i

Graph

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