de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

wurzeln von z^6-2z^3+2

Lösung

wurzeln von

z^{6} - 2 z^{3} + 2

Lösung

z = \frac{2 ^{\frac{2}{3}} ( 1 + 3 )}{4} + i \frac{2 ^{\frac{2}{3}} ( - 1 + 3 )}{4}, z = - \frac{2 ^{\frac{2}{3}}}{2} + i \frac{2 ^{\frac{2}{3}}}{2}, z = \frac{2 ^{\frac{2}{3}} ( 1 - 3 )}{4} + i \frac{2 ^{\frac{2}{3}} ( - 1 - 3 )}{4}, z = \frac{2 ^{\frac{2}{3}} ( 1 + 3 )}{4} + i \frac{2 ^{\frac{2}{3}} ( 1 - 3 )}{4}, z = - \frac{2 ^{\frac{2}{3}} ( - 1 + 3 )}{4} + i \frac{2 ^{\frac{2}{3}} ( 1 + 3 )}{4}, z = - \frac{2 ^{\frac{2}{3}}}{2} - i \frac{2 ^{\frac{2}{3}}}{2}

Schritte zur Lösung

z^{6} - 2 z^{3} + 2

Die Wurzeln sind die Schnittpunkte mit der x-Achse

(y = 0)

z^{6} - 2 z^{3} + 2 = 0

Schreibe die Gleichung um mit

u = z^{3}

und

u^{2} = z^{6}

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

Löse

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

u = 1 + i, u = 1 - i

Setze

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

löse für

z

Löse

z^{3} = 1 + i : z = \frac{2 ^{\frac{2}{3}} ( 1 + 3 )}{4} + i \frac{2 ^{\frac{2}{3}} ( - 1 + 3 )}{4}, z = - \frac{2 ^{\frac{2}{3}}}{2} + i \frac{2 ^{\frac{2}{3}}}{2}, z = \frac{2 ^{\frac{2}{3}} ( 1 - 3 )}{4} + i \frac{2 ^{\frac{2}{3}} ( - 1 - 3 )}{4}

Löse

z^{3} = 1 - i : z = \frac{2 ^{\frac{2}{3}} ( 1 + 3 )}{4} + i \frac{2 ^{\frac{2}{3}} ( 1 - 3 )}{4}, z = - \frac{2 ^{\frac{2}{3}} ( - 1 + 3 )}{4} + i \frac{2 ^{\frac{2}{3}} ( 1 + 3 )}{4}, z = - \frac{2 ^{\frac{2}{3}}}{2} - i \frac{2 ^{\frac{2}{3}}}{2}

Die Lösungen sind

z = \frac{2 ^{\frac{2}{3}} ( 1 + 3 )}{4} + i \frac{2 ^{\frac{2}{3}} ( - 1 + 3 )}{4}, z = - \frac{2 ^{\frac{2}{3}}}{2} + i \frac{2 ^{\frac{2}{3}}}{2}, z = \frac{2 ^{\frac{2}{3}} ( 1 - 3 )}{4} + i \frac{2 ^{\frac{2}{3}} ( - 1 - 3 )}{4}, z = \frac{2 ^{\frac{2}{3}} ( 1 + 3 )}{4} + i \frac{2 ^{\frac{2}{3}} ( 1 - 3 )}{4}, z = - \frac{2 ^{\frac{2}{3}} ( - 1 + 3 )}{4} + i \frac{2 ^{\frac{2}{3}} ( 1 + 3 )}{4}, z = - \frac{2 ^{\frac{2}{3}}}{2} - i \frac{2 ^{\frac{2}{3}}}{2}

Graph

Beliebte Beispiele

wurzeln von x^3-1=0

x^3-10x^2+19x+30=0