a^3=2+sqrt(5)

Lösung

a^{3} = 2 + 5

a = 3 2 + 5, a = - 3 2 + 5 \frac{1}{2} + 3 2 + 5 \frac{3}{2} i, a = - 3 2 + 5 \frac{1}{2} - 3 2 + 5 \frac{3}{2} i

Schritte zur Lösung

a^{3} = 2 + 5

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 = 3 2 + 5, a = 3 2 + 5 \frac{- 1 + 3 i}{2}, a = 3 2 + 5 \frac{- 1 - 3 i}{2}

Vereinfache

3 2 + 5 \frac{- 1 + 3 i}{2} : - 3 2 + 5 \frac{1}{2} + 3 2 + 5 \frac{3}{2} i

Vereinfache

3 2 + 5 \frac{- 1 - 3 i}{2} : - 3 2 + 5 \frac{1}{2} - 3 2 + 5 \frac{3}{2} i

a = 3 2 + 5, a = - 3 2 + 5 \frac{1}{2} + 3 2 + 5 \frac{3}{2} i, a = - 3 2 + 5 \frac{1}{2} - 3 2 + 5 \frac{3}{2} i

(x + 2)^{2} \frac{2 x - 5}{3} = 3

5 x^{6} - (3 - 2 x) 8 = (4 x - 3) 12

x^{3} - 6 x^{2} - 15 x + 90 = 0

so l v e f or x, 4 x^{3} + 4 y = 0

3 x^{3} + 9 x^{2} + 8 x = 0