12=305*x^3

Lösung

12 = 305 \cdot x^{3}

x = 3 \frac{12}{305}, x = - 3 \frac{12}{305} \frac{1}{2} + 3 \frac{12}{305} \frac{3}{2} i, x = - 3 \frac{12}{305} \frac{1}{2} - 3 \frac{12}{305} \frac{3}{2} i

Schritte zur Lösung

12 = 305 x^{3}

Tausche die Seiten

305 x^{3} = 12

Teile beide Seiten durch

305

x^{3} = \frac{12}{305}

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{12}{305}, x = 3 \frac{12}{305} \frac{- 1 + 3 i}{2}, x = 3 \frac{12}{305} \frac{- 1 - 3 i}{2}

Vereinfache

3 \frac{12}{305} \frac{- 1 + 3 i}{2} : - 3 \frac{12}{305} \frac{1}{2} + 3 \frac{12}{305} \frac{3}{2} i

Vereinfache

3 \frac{12}{305} \frac{- 1 - 3 i}{2} : - 3 \frac{12}{305} \frac{1}{2} - 3 \frac{12}{305} \frac{3}{2} i

x = 3 \frac{12}{305}, x = - 3 \frac{12}{305} \frac{1}{2} + 3 \frac{12}{305} \frac{3}{2} i, x = - 3 \frac{12}{305} \frac{1}{2} - 3 \frac{12}{305} \frac{3}{2} i

so l v e f or x, x^{3} - 2 x^{2} - 9 x = 18

x = (3 x^{2} + 2)^{2}

x^{3} + 3 x^{2} + 18 x = 0

625 = x^{4}

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