19x^3=216

Lösung

19 x^{3} = 216

x = \frac{6}{3 19}, x = \frac{6 ( - \frac{1}{2} + \frac{3}{2} i )}{3 19}, x = \frac{6 ( - \frac{1}{2} - \frac{3}{2} i )}{3 19}

Schritte zur Lösung

19 x^{3} = 216

Teile beide Seiten durch

19

x^{3} = \frac{216}{19}

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{216}{19}, x = 3 \frac{216}{19} \frac{- 1 + 3 i}{2}, x = 3 \frac{216}{19} \frac{- 1 - 3 i}{2}

3 \frac{216}{19} = \frac{6}{3 19}

Vereinfache

3 \frac{216}{19} \frac{- 1 + 3 i}{2} : \frac{6 ( - \frac{1}{2} + \frac{3}{2} i )}{3 19}

Vereinfache

3 \frac{216}{19} \frac{- 1 - 3 i}{2} : \frac{6 ( - \frac{1}{2} - \frac{3}{2} i )}{3 19}

x = \frac{6}{3 19}, x = \frac{6 ( - \frac{1}{2} + \frac{3}{2} i )}{3 19}, x = \frac{6 ( - \frac{1}{2} - \frac{3}{2} i )}{3 19}

x^{4} - 40 x^{2} + 144 = 0

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

2 x^{3} + x^{2} + 25 = 0

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

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