n^3=125

Lösung

n^{3} = 125

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

Schritte zur Lösung

n^{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}

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

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

(x + 2) (x - 3) (x + 1) (x + 6) = - 36

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

4 x^{5} + 5 x^{2} - 3 x = 0

16 x^{4} + 8 x^{2} - 3 = 0

x^{3} - 3 x^{2} + 3 x - 6 = 0