de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

4z^4+2z^2+1=0

Lösung

4 z^{4} + 2 z^{2} + 1 = 0

Lösung

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

Schritte zur Lösung

4 z^{4} + 2 z^{2} + 1 = 0

Schreibe die Gleichung um mit

u = z^{2}

und

u^{2} = z^{4}

4 u^{2} + 2 u + 1 = 0

Löse

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

u = - \frac{1}{4} + i \frac{3}{4}, u = - \frac{1}{4} - i \frac{3}{4}

Setze

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

löse für

z

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

x^{3} - 3 x - 18 = 0

x^3+5x^2+4x+5=0

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

solvefor y,x=y^5-2

so l v e f or y, x = y^{5} - 2

solvefor x,x=x^3-2x+5+x

so l v e f or x, x = x^{3} - 2 x + 5 + x

24 x^{4} - 2 x^{2} - 1 = 0