z^3=125

Lösung

z^{3} = 125

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

Schritte zur Lösung

z^{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}

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

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

x (x - 1)^{2} + 14 (x - 1)^{3} = 0

x^{4} = 6

x^{4} - 4 x^{3} + x^{2} + 6 x = 0

3 x^{4} + 16 x^{2} + 17 = 0

z^{3} = - 64