de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

12x^4-4x^2-1=0

Lösung

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

Lösung

x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{1}{6} i, x = - \frac{1}{6} i

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

12 u^{2} - 4 u - 1 = 0

Löse

12 u^{2} - 4 u - 1 = 0 : u = \frac{1}{2}, u = - \frac{1}{6}

u = \frac{1}{2}, u = - \frac{1}{6}

Setze

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

löse für

x

Löse

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

Löse

x^{2} = - \frac{1}{6} : x = \frac{1}{6} i, x = - \frac{1}{6} i

Die Lösungen sind

x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{1}{6} i, x = - \frac{1}{6} i

Graph

Beliebte Beispiele

2 - x = x^{3}

(x^2-6)(x^2+1)=0

(x^{2} - 6) (x^{2} + 1) = 0

x^{4} + 16 = 2 x^{3} + 8 x

4x^3+8x^2-9x=18

4 x^{3} + 8 x^{2} - 9 x = 18

x^{2} (2 x^{2} + 6) = 8