x^3= 8/343

Lösung

x^{3} = \frac{8}{343}

x = \frac{2}{7}, x = - \frac{1}{7} + \frac{3}{7} i, x = - \frac{1}{7} - \frac{3}{7} i

Schritte zur Lösung

x^{3} = \frac{8}{343}

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}

x = 3 \frac{8}{343}, x = 3 \frac{8}{343} \frac{- 1 + 3 i}{2}, x = 3 \frac{8}{343} \frac{- 1 - 3 i}{2}

3 \frac{8}{343} = \frac{2}{7}

Vereinfache

3 \frac{8}{343} \frac{- 1 + 3 i}{2} : - \frac{1}{7} + \frac{3}{7} i

Vereinfache

3 \frac{8}{343} \frac{- 1 - 3 i}{2} : - \frac{1}{7} - \frac{3}{7} i

x = \frac{2}{7}, x = - \frac{1}{7} + \frac{3}{7} i, x = - \frac{1}{7} - \frac{3}{7} i

8 x^{10} - x^{4} - 2 = 0

(r)^{3} = 216

x^{3} + x^{2} + x = - 1

64 x^{3} + 216 (x - 1)^{3} = 0

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