m^3= 8/27

Lösung

m^{3} = \frac{8}{27}

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

Schritte zur Lösung

m^{3} = \frac{8}{27}

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}

m = 3 \frac{8}{27}, m = 3 \frac{8}{27} \frac{- 1 + 3 i}{2}, m = 3 \frac{8}{27} \frac{- 1 - 3 i}{2}

3 \frac{8}{27} = \frac{2}{3}

Vereinfache

3 \frac{8}{27} \frac{- 1 + 3 i}{2} : - \frac{1}{3} + \frac{1}{3} i

Vereinfache

3 \frac{8}{27} \frac{- 1 - 3 i}{2} : - \frac{1}{3} - \frac{1}{3} i

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

25 x^{4} + 4 = 29 x^{2}

8 x^{3} + 3 x^{2} - 16 x - 1 = 0

x = x^{5}

x^{3} - 8 x^{2} - 15 = 0

20 x^{3} + 100 x^{2} + 120 x = 0