u^3=-18

Lösung

u^{3} = - 18

u = - 318, u = - \frac{3 9 ( - 1 + 3 i )}{3 2 ^{2}}, u = - \frac{3 9 ( - 1 - 3 i )}{3 2 ^{2}}

Schritte zur Lösung

u^{3} = - 18

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}

u = 3 - 18, u = 3 - 18 \frac{- 1 + 3 i}{2}, u = 3 - 18 \frac{- 1 - 3 i}{2}

3 - 18 = - 318

Vereinfache

3 - 18 \frac{- 1 + 3 i}{2} : - \frac{3 9 ( - 1 + 3 i )}{3 2 ^{2}}

Vereinfache

3 - 18 \frac{- 1 - 3 i}{2} : - \frac{3 9 ( - 1 - 3 i )}{3 2 ^{2}}

u = - 318, u = - \frac{3 9 ( - 1 + 3 i )}{3 2 ^{2}}, u = - \frac{3 9 ( - 1 - 3 i )}{3 2 ^{2}}

x^{4} - 4 x^{2} - 77 = 0

((x - 2)^{2})^{2} - 2 (x - 2)^{2} = 0

u^{3} = - 23

0 = 3 x^{3} - 3 x^{2} - 18 x

x^{4} - 64 i = 0