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Beliebt Algebra >

x^5x-6=39

Lösung

x^{5} x - 6 = 39

Lösung

x = 345, x = - 345, x = \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} + \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} - \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} - \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} + \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i

Schritte zur Lösung

x^{5} x - 6 = 39

Verschiebe

6

auf die rechte Seite

x^{5} x = 45

Vereinfache

x^{6} = 45

Schreibe die Gleichung um mit

u = x^{2}

und

u^{3} = x^{6}

u^{3} = 45

Löse

u^{3} = 45 : u = 345, u = 345 \frac{- 1 + 3 i}{2}, u = 345 \frac{- 1 - 3 i}{2}

u = 345, u = 345 \frac{- 1 + 3 i}{2}, u = 345 \frac{- 1 - 3 i}{2}

Setze

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

löse für

x

Löse

x^{2} = 345 : x = 345, x = - 345

Löse

x^{2} = 345 \frac{- 1 + 3 i}{2} : x = \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} + \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} - \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i

Löse

x^{2} = 345 \frac{- 1 - 3 i}{2} : x = \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} - \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} + \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i

Die Lösungen sind

x = 345, x = - 345, x = \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} + \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} - \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} - \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} + \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i

Graph

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