a^3=78

Lösung

a^{3} = 78

a = 378, a = - 378 \frac{1}{2} + 378 \frac{3}{2} i, a = - 378 \frac{1}{2} - 378 \frac{3}{2} i

Schritte zur Lösung

a^{3} = 78

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}

a = 378, a = 378 \frac{- 1 + 3 i}{2}, a = 378 \frac{- 1 - 3 i}{2}

Vereinfache

378 \frac{- 1 + 3 i}{2} : - 378 \frac{1}{2} + 378 \frac{3}{2} i

Vereinfache

378 \frac{- 1 - 3 i}{2} : - 378 \frac{1}{2} - 378 \frac{3}{2} i

a = 378, a = - 378 \frac{1}{2} + 378 \frac{3}{2} i, a = - 378 \frac{1}{2} - 378 \frac{3}{2} i

3 x^{5} - 20 x^{3} = 0

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

(X - 2) (X + 4) (X - 5) = 0

5 x^{4} = 80 x^{2}

- 3 x^{3} + 75 x = 0