x^3=-125

Lösung

x^{3} = - 125

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

Schritte zur Lösung

x^{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}

x = 3 - 125, x = 3 - 125 \frac{- 1 + 3 i}{2}, x = 3 - 125 \frac{- 1 - 3 i}{2}

3 - 125 = - 5

Vereinfache

3 - 125 \frac{- 1 + 3 i}{2} : \frac{5}{2} - \frac{5 3}{2} i

Vereinfache

3 - 125 \frac{- 1 - 3 i}{2} : \frac{5}{2} + \frac{5 3}{2} i

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

(x + 5) (x^{2} - 4) = 0

(x^{2} - 5 x)^{2} - 7 (x^{2} - 5 x) + 6 = 0

n^{3} - n - 990 = 0

x^{3} - 3 x^{2} - 25 x + 75 = 0

2 x = (35 x^{6}) - 178