de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

x^6-65x^3+64=0

Lösung

x^{6} - 65 x^{3} + 64 = 0

Lösung

x = 4, x = - 2 + 23 i, x = - 2 - 23 i, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

Schritte zur Lösung

x^{6} - 65 x^{3} + 64 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} - 65 u + 64 = 0

Löse

u^{2} - 65 u + 64 = 0 : u = 64, u = 1

u = 64, u = 1

Setze

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

löse für

x

Löse

x^{3} = 64 : x = 4, x = - 2 + 23 i, x = - 2 - 23 i

Löse

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

Die Lösungen sind

x = 4, x = - 2 + 23 i, x = - 2 - 23 i, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

Graph

Beliebte Beispiele

z^{6} + 4 z^{3} + 16 = 0

x^{3} - a^{2} x = 0

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

-x^3+2x^2+5x-6=0

- x^{3} + 2 x^{2} + 5 x - 6 = 0

x^{8} - 1 = 0