m^3= 1/125

Lösung

m^{3} = \frac{1}{125}

m = \frac{1}{5}, m = - \frac{1}{10} + \frac{3}{10} i, m = - \frac{1}{10} - \frac{3}{10} i

Schritte zur Lösung

m^{3} = \frac{1}{125}

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{1}{125}, m = 3 \frac{1}{125} \frac{- 1 + 3 i}{2}, m = 3 \frac{1}{125} \frac{- 1 - 3 i}{2}

3 \frac{1}{125} = \frac{1}{5}

Vereinfache

3 \frac{1}{125} \frac{- 1 + 3 i}{2} : - \frac{1}{10} + \frac{3}{10} i

Vereinfache

3 \frac{1}{125} \frac{- 1 - 3 i}{2} : - \frac{1}{10} - \frac{3}{10} i

m = \frac{1}{5}, m = - \frac{1}{10} + \frac{3}{10} i, m = - \frac{1}{10} - \frac{3}{10} i

2 x^{4} + 6 x^{3} - 8 x^{2} - 24 x = 0

2 x (x^{3} - 216) = 0

x^{4} + 2 x^{3} - 14 x^{2} + 2 x + 1 = 0

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

125000 (x)^{6} = 165000