k^3=729

Lösung

k^{3} = 729

k = 9, k = - \frac{9}{2} + \frac{9 3}{2} i, k = - \frac{9}{2} - \frac{9 3}{2} i

Schritte zur Lösung

k^{3} = 729

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}

k = 3729, k = 3729 \frac{- 1 + 3 i}{2}, k = 3729 \frac{- 1 - 3 i}{2}

3729 = 9

Vereinfache

3729 \frac{- 1 + 3 i}{2} : - \frac{9}{2} + \frac{9 3}{2} i

Vereinfache

3729 \frac{- 1 - 3 i}{2} : - \frac{9}{2} - \frac{9 3}{2} i

k = 9, k = - \frac{9}{2} + \frac{9 3}{2} i, k = - \frac{9}{2} - \frac{9 3}{2} i

0 = - 25 x^{4} + 9 x^{2}

x^{3} - 3 x^{2} - 10 x + 30 = 0

so l v e f or x, y^{2} + 24 = x^{3}

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

3 x^{3} - 3 = 0