x^3=2^{-3}

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

2^{- 3} : \frac{1}{8}

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

3 \frac{1}{8} = \frac{1}{2}

Vereinfache

3 \frac{1}{8} \frac{- 1 + 3 i}{2} : - \frac{1}{4} + \frac{3}{4} i

Vereinfache

3 \frac{1}{8} \frac{- 1 - 3 i}{2} : - \frac{1}{4} - \frac{3}{4} i

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

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

so l v e f or x, x^{4} + y^{4} + 2 = 0

- x^{4} + 8 x^{3} - 18 x^{2} = 0

- x^{3} + 10 x^{2} - 29 x + 20 = 0

69 = c^{3}