de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

z^8-2z^4+4=0

Lösung

z^{8} - 2 z^{4} + 4 = 0

Lösung

z = \frac{1}{2 2 2 - 6} + \frac{2 2 - 6}{2} i, z = - \frac{1}{2 2 2 - 6} - \frac{2 2 - 6}{2} i, z = - \frac{1}{2 6 + 2 2} + \frac{6 + 2 2}{2} i, z = - \frac{1}{2 ( - 6 + 2 2 )} - \frac{6 + 2 2}{2} i, z = \frac{1}{2 6 + 2 2} + \frac{6 + 2 2}{2} i, z = - \frac{1}{2 6 + 2 2} - \frac{6 + 2 2}{2} i, z = - \frac{1}{2 2 2 - 6} + \frac{2 2 - 6}{2} i, z = - \frac{1}{2 ( - 2 2 - 6 )} - \frac{2 2 - 6}{2} i

Schritte zur Lösung

z^{8} - 2 z^{4} + 4 = 0

Schreibe die Gleichung um mit

u = z^{2}, u^{2} = z^{4}

und

u^{4} = z^{8}

u^{4} - 2 u^{2} + 4 = 0

Löse

u^{4} - 2 u^{2} + 4 = 0 : u = \frac{3}{2} + \frac{1}{2} i, u = - \frac{3}{2} - \frac{1}{2} i, u = - \frac{3}{2} + \frac{1}{2} i, u = \frac{3}{2} - \frac{1}{2} i

u = \frac{3}{2} + \frac{1}{2} i, u = - \frac{3}{2} - \frac{1}{2} i, u = - \frac{3}{2} + \frac{1}{2} i, u = \frac{3}{2} - \frac{1}{2} i

Setze

u = z^{2} w i e d er e in,

löse für

z

Löse

z^{2} = \frac{3}{2} + \frac{1}{2} i : z = \frac{1}{2 2 2 - 6} + \frac{2 2 - 6}{2} i, z = - \frac{1}{2 2 2 - 6} - \frac{2 2 - 6}{2} i

Löse

z^{2} = - \frac{3}{2} - \frac{1}{2} i : z = - \frac{1}{2 6 + 2 2} + \frac{6 + 2 2}{2} i, z = - \frac{1}{2 ( - 6 + 2 2 )} - \frac{6 + 2 2}{2} i

Löse

z^{2} = - \frac{3}{2} + \frac{1}{2} i : z = \frac{1}{2 6 + 2 2} + \frac{6 + 2 2}{2} i, z = - \frac{1}{2 6 + 2 2} - \frac{6 + 2 2}{2} i

Löse

z^{2} = \frac{3}{2} - \frac{1}{2} i : z = - \frac{1}{2 2 2 - 6} + \frac{2 2 - 6}{2} i, z = - \frac{1}{2 ( - 2 2 - 6 )} - \frac{2 2 - 6}{2} i

Die Lösungen sind

z = \frac{1}{2 2 2 - 6} + \frac{2 2 - 6}{2} i, z = - \frac{1}{2 2 2 - 6} - \frac{2 2 - 6}{2} i, z = - \frac{1}{2 6 + 2 2} + \frac{6 + 2 2}{2} i, z = - \frac{1}{2 ( - 6 + 2 2 )} - \frac{6 + 2 2}{2} i, z = \frac{1}{2 6 + 2 2} + \frac{6 + 2 2}{2} i, z = - \frac{1}{2 6 + 2 2} - \frac{6 + 2 2}{2} i, z = - \frac{1}{2 2 2 - 6} + \frac{2 2 - 6}{2} i, z = - \frac{1}{2 ( - 2 2 - 6 )} - \frac{2 2 - 6}{2} i

Graph

Beliebte Beispiele

(x^2+2x)^2-2(x^2+2x)-3=0

4x^3-15x^2+12x=0

12x^3-91x^2+50x-7=0

wurzeln von x^3+3x^2-4x-12