de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

4x^4-10x^2+9=0

Lösung

4 x^{4} - 10 x^{2} + 9 = 0

Lösung

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

Schritte zur Lösung

4 x^{4} - 10 x^{2} + 9 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

4 u^{2} - 10 u + 9 = 0

Löse

4 u^{2} - 10 u + 9 = 0 : u = \frac{5}{4} + i \frac{11}{4}, u = \frac{5}{4} - i \frac{11}{4}

u = \frac{5}{4} + i \frac{11}{4}, u = \frac{5}{4} - i \frac{11}{4}

Setze

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

löse für

x

Löse

x^{2} = \frac{5}{4} + i \frac{11}{4} : x = \frac{11}{2 2} + \frac{1}{2 2} i, x = - \frac{11}{2 2} - \frac{1}{2 2} i

Löse

x^{2} = \frac{5}{4} - i \frac{11}{4} : x = \frac{11}{2 2} - \frac{1}{2 2} i, x = - \frac{11}{2 2} + \frac{1}{2 2} i

Die Lösungen sind

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

Graph

Beliebte Beispiele

x^{5} = \frac{1}{32}

(x^{2} - 7)^{2} = 25

solvefor x,x^3=y^2

so l v e f or x, x^{3} = y^{2}

0 = 4 x^{3} - 16 x

(x+1)(x+2)(x+3)=0

(x + 1) (x + 2) (x + 3) = 0