m^3=1

Lösung

m^{3} = 1

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

Schritte zur Lösung

m^{3} = 1

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

Vereinfache

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

Vereinfache

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

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

roo t s r^{3} - 3 r^{2} + 3 r - 1

x^{3} - 3 x^{2} - 40 x = 0

(x^{2} + 25)^{2} = 0

so l v e f or y, x^{3} + y^{3} = 0

x^{5} + 2 x^{3} + 10 x^{2} + x + 10 = 0