4x^3=48,x

Lösung

4 x^{3} = 48, x

x = 312, x = - 312 \frac{1}{2} + 312 \frac{3}{2} i, x = - 312 \frac{1}{2} - 312 \frac{3}{2} i

Schritte zur Lösung

4 x^{3} = 48, x

Teile beide Seiten durch

4

x^{3} = 12

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}

x = 312, x = 312 \frac{- 1 + 3 i}{2}, x = 312 \frac{- 1 - 3 i}{2}

Vereinfache

312 \frac{- 1 + 3 i}{2} : - 312 \frac{1}{2} + 312 \frac{3}{2} i

Vereinfache

312 \frac{- 1 - 3 i}{2} : - 312 \frac{1}{2} - 312 \frac{3}{2} i

x = 312, x = - 312 \frac{1}{2} + 312 \frac{3}{2} i, x = - 312 \frac{1}{2} - 312 \frac{3}{2} i

0 = 3 x^{4} + 4 x^{3} - 12 x^{2} + 12

15 x^{4} + 7 x^{2} - 2 = 0

x^{3} - 5 x^{2} + 3 x = \frac{1}{2}

2 x^{3} - 3 x^{2} - 2 x + 3 = x^{2} - 1

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