u^3=125

Lösung

u^{3} = 125

u = 5, u = - \frac{5}{2} + \frac{5 3}{2} i, u = - \frac{5}{2} - \frac{5 3}{2} i

Schritte zur Lösung

u^{3} = 125

Für

x^{3} = f (a)

sind die Lösungen

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

u = 3125, u = 3125 \frac{- 1 + 3 i}{2}, u = 3125 \frac{- 1 - 3 i}{2}

3125 = 5

Vereinfache

3125 \frac{- 1 + 3 i}{2} : - \frac{5}{2} + \frac{5 3}{2} i

Vereinfache

3125 \frac{- 1 - 3 i}{2} : - \frac{5}{2} - \frac{5 3}{2} i

u = 5, u = - \frac{5}{2} + \frac{5 3}{2} i, u = - \frac{5}{2} - \frac{5 3}{2} i

36 x^{4} + 16 = 52 x^{2}

so l v e f or a, y = a^{3}

2 x^{3} + 4 x^{2} - 2 x - 4 = 0

x^{3} - 5 x^{2} - 14 x = 0

4 x^{4} + 45 x^{2} + 81 = 0