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

Lösung

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

x = 5, x = - \frac{5}{2} + \frac{5 3}{2} i, x = - \frac{5}{2} - \frac{5 3}{2} i, x = - 3 \frac{371}{3}, x = - \frac{3 371 ( - 1 + 3 i )}{2 3 3}, x = - \frac{3 371 ( - 1 - 3 i )}{2 3 3}

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

3 u^{2} - 4 u - 46375 = 0

Löse

3 u^{2} - 4 u - 46375 = 0 : u = 125, u = - \frac{371}{3}

u = 125, u = - \frac{371}{3}

Setze

u = x^{3} w i e d er e in,

löse für

x

Löse

x^{3} = 125 : x = 5, x = - \frac{5}{2} + \frac{5 3}{2} i, x = - \frac{5}{2} - \frac{5 3}{2} i

Löse

x^{3} = - \frac{371}{3} : x = - 3 \frac{371}{3}, x = - \frac{3 371 ( - 1 + 3 i )}{2 3 3}, x = - \frac{3 371 ( - 1 - 3 i )}{2 3 3}

Die Lösungen sind

x = 5, x = - \frac{5}{2} + \frac{5 3}{2} i, x = - \frac{5}{2} - \frac{5 3}{2} i, x = - 3 \frac{371}{3}, x = - \frac{3 371 ( - 1 + 3 i )}{2 3 3}, x = - \frac{3 371 ( - 1 - 3 i )}{2 3 3}

2 x^{3} + 5 x^{2} + 4 x + 1 = 0

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x^{4} - 6 x^{3} + 7 x^{2} - 6 x + 1 = 0