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Beliebt Algebra >

5=k^6

Lösung

5 = k^{6}

Lösung

k = 35, k = - 35, k = \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} + \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, k = - \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} - \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, k = \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} - \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, k = - \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} + \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i

Schritte zur Lösung

5 = k^{6}

Tausche die Seiten

k^{6} = 5

Schreibe die Gleichung um mit

u = k^{2}

und

u^{3} = k^{6}

u^{3} = 5

Löse

u^{3} = 5 : u = 35, u = 35 \frac{- 1 + 3 i}{2}, u = 35 \frac{- 1 - 3 i}{2}

u = 35, u = 35 \frac{- 1 + 3 i}{2}, u = 35 \frac{- 1 - 3 i}{2}

Setze

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

löse für

k

Löse

k^{2} = 35 : k = 35, k = - 35

Löse

k^{2} = 35 \frac{- 1 + 3 i}{2} : k = \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} + \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, k = - \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} - \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i

Löse

k^{2} = 35 \frac{- 1 - 3 i}{2} : k = \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} - \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, k = - \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} + \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i

Die Lösungen sind

k = 35, k = - 35, k = \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} + \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, k = - \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} - \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, k = \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} - \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, k = - \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} + \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i

Graph

Beliebte Beispiele

z^{4} = 3 + 2 i

0 = x^{3} + 8

x^4-12x^3+48x^2-73x+36=0

x^{4} - 12 x^{3} + 48 x^{2} - 73 x + 36 = 0

0 = x^{3} - 4

- 2 x^{3} + x^{2} = 0