r^3= 3/9

Lösung

r^{3} = \frac{3}{9}

r = \frac{1}{3 3}, r = - \frac{1}{2 3 3} + \frac{6 3}{2} i, r = - \frac{1}{2 3 3} - \frac{6 3}{2} i

Schritte zur Lösung

r^{3} = \frac{3}{9}

Streiche die gemeinsamen Faktoren:

3

r^{3} = \frac{1}{3}

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}

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

3 \frac{1}{3} = \frac{1}{3 3}

Vereinfache

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

Vereinfache

3 \frac{1}{3} \frac{- 1 - 3 i}{2} : - \frac{1}{2 3 3} - \frac{6 3}{2} i

r = \frac{1}{3 3}, r = - \frac{1}{2 3 3} + \frac{6 3}{2} i, r = - \frac{1}{2 3 3} - \frac{6 3}{2} i

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

3 x^{4} + 8 x^{3} + 6 x^{2} + 3 x - 2 = 0

2 x^{4} - 200 x^{2} = 0

x^{3} - 5 x - 2 = 0

x^{3} - 3 x^{2} + 24 = 0