3x^3-2=0

Lösung

3 x^{3} - 2 = 0

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

Schritte zur Lösung

3 x^{3} - 2 = 0

Verschiebe

2

auf die rechte Seite

3 x^{3} = 2

Teile beide Seiten durch

3

x^{3} = \frac{2}{3}

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

Vereinfache

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

Vereinfache

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

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

x^{4} - 6 x^{2} + 8 x - 1 = 0

so l v e f or a, (a - b)^{3} = 0

x^{3} - 30 x^{2} + 1 5^{3} = 0

- 10 x^{4} + 6 = 0

3 x^{6} - 4 x^{3} - 46375 = 0