z^3=4-4sqrt(3)+0i

Lösung

z^{3} = 4 - 43 + 0 i

z = 3 4 - 43, z = - 3 4 - 43 \frac{1}{2} + 3 4 - 43 \frac{3}{2} i, z = - 3 4 - 43 \frac{1}{2} - 3 4 - 43 \frac{3}{2} i

Schritte zur Lösung

z^{3} = 4 - 43 + 0 i

Vereinfache

4 - 43 + 0 i : 4 - 43

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 = 3 4 - 43, z = 3 4 - 43 \frac{- 1 + 3 i}{2}, z = 3 4 - 43 \frac{- 1 - 3 i}{2}

Vereinfache

3 4 - 43 \frac{- 1 + 3 i}{2} : - 3 4 - 43 \frac{1}{2} + 3 4 - 43 \frac{3}{2} i

Vereinfache

3 4 - 43 \frac{- 1 - 3 i}{2} : - 3 4 - 43 \frac{1}{2} - 3 4 - 43 \frac{3}{2} i

z = 3 4 - 43, z = - 3 4 - 43 \frac{1}{2} + 3 4 - 43 \frac{3}{2} i, z = - 3 4 - 43 \frac{1}{2} - 3 4 - 43 \frac{3}{2} i

12 = \frac{1}{2} a^{21} a

x^{3} - 3 x^{2} + 9 x + 13 = 0

x^{8} + 35 x^{4} = 36

x (3 x^{2} - 2 x - 12 x + 8) = 0

so l v e f or x, x^{3} + y^{3} + z^{3} = 1