y^3=-125

Lösung

y^{3} = - 125

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

Schritte zur Lösung

y^{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}

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

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

x^{3} + 3 x^{2} - 25 x + 21 = 0

(x^{2} + 2 x)^{2} = 2 x^{2} + 4 x + 3

p^{3} - 144 p = 0

x^{3} - 9 x^{2} - 22 x = 0

x^{3} + 2 x^{2} - 7 x = - 4