w^3=-12

Lösung

w^{3} = - 12

w = - 312, w = \frac{3 3}{3 2} - \frac{6 3 ^{5}}{3 2} i, w = \frac{3 3}{3 2} + \frac{6 3 ^{5}}{3 2} i

Schritte zur Lösung

w^{3} = - 12

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}

w = 3 - 12, w = 3 - 12 \frac{- 1 + 3 i}{2}, w = 3 - 12 \frac{- 1 - 3 i}{2}

3 - 12 = - 312

Vereinfache

3 - 12 \frac{- 1 + 3 i}{2} : \frac{3 3}{3 2} - \frac{6 3 ^{5}}{3 2} i

Vereinfache

3 - 12 \frac{- 1 - 3 i}{2} : \frac{3 3}{3 2} + \frac{6 3 ^{5}}{3 2} i

w = - 312, w = \frac{3 3}{3 2} - \frac{6 3 ^{5}}{3 2} i, w = \frac{3 3}{3 2} + \frac{6 3 ^{5}}{3 2} i

x^{3} + 5 x^{2} + 7 x = 0

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

4 x^{3} + 12 x^{2} + 16 x = 0

x^{4} - 6 x^{3} + 6 x^{2} - 6 x + 5 = 0

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