q^3= 1/343

Lösung

q^{3} = \frac{1}{343}

q = \frac{1}{7}, q = - \frac{1}{14} + \frac{3}{14} i, q = - \frac{1}{14} - \frac{3}{14} i

Schritte zur Lösung

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

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

3 \frac{1}{343} = \frac{1}{7}

Vereinfache

3 \frac{1}{343} \frac{- 1 + 3 i}{2} : - \frac{1}{14} + \frac{3}{14} i

Vereinfache

3 \frac{1}{343} \frac{- 1 - 3 i}{2} : - \frac{1}{14} - \frac{3}{14} i

q = \frac{1}{7}, q = - \frac{1}{14} + \frac{3}{14} i, q = - \frac{1}{14} - \frac{3}{14} i

x^{4} - 3 x^{3} - x^{2} + 9 x - 6 = 0

0 = (x + 3) (x^{2} + 4)

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

- 8 m^{5} + 24 = 0

(\frac{1 + r}{100})^{10} = 1.5775