de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

x^4-x^2+3=0

Lösung

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

Lösung

x = \frac{1 + 2 3}{2} + \frac{11}{2 1 + 2 3} i, x = - \frac{1 + 2 3}{2} - \frac{11}{2 1 + 2 3} i, x = \frac{1 + 2 3}{2} - \frac{11}{2 1 + 2 3} i, x = - \frac{1 + 2 3}{2} + \frac{11}{2 1 + 2 3} i

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - u + 3 = 0

Löse

u^{2} - u + 3 = 0 : u = \frac{1}{2} + i \frac{11}{2}, u = \frac{1}{2} - i \frac{11}{2}

u = \frac{1}{2} + i \frac{11}{2}, u = \frac{1}{2} - i \frac{11}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{1}{2} + i \frac{11}{2} : x = \frac{1 + 2 3}{2} + \frac{11}{2 1 + 2 3} i, x = - \frac{1 + 2 3}{2} - \frac{11}{2 1 + 2 3} i

Löse

x^{2} = \frac{1}{2} - i \frac{11}{2} : x = \frac{1 + 2 3}{2} - \frac{11}{2 1 + 2 3} i, x = - \frac{1 + 2 3}{2} + \frac{11}{2 1 + 2 3} i

Die Lösungen sind

x = \frac{1 + 2 3}{2} + \frac{11}{2 1 + 2 3} i, x = - \frac{1 + 2 3}{2} - \frac{11}{2 1 + 2 3} i, x = \frac{1 + 2 3}{2} - \frac{11}{2 1 + 2 3} i, x = - \frac{1 + 2 3}{2} + \frac{11}{2 1 + 2 3} i

Graph

Beliebte Beispiele

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

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

4 = x^{10}

0 = x^{4} - 7 x^{2} + 12

x^{5} = a^{3}

x^{3} = \frac{8}{1 1 ^{3}}