de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

x^8+24x^4=25

Lösung

x^{8} + 24 x^{4} = 25

Lösung

x = 1, x = - 1, x = i, x = - i, x = \frac{5}{2} + \frac{5}{2} i, x = - \frac{5}{2} - \frac{5}{2} i, x = \frac{5}{2} - \frac{5}{2} i, x = - \frac{5}{2} + \frac{5}{2} i

Schritte zur Lösung

x^{8} + 24 x^{4} = 25

Verschiebe

25

auf die linke Seite

x^{8} + 24 x^{4} - 25 = 0

Schreibe die Gleichung um mit

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

und

u^{4} = x^{8}

u^{4} + 24 u^{2} - 25 = 0

Löse

u^{4} + 24 u^{2} - 25 = 0 : u = 1, u = - 1, u = 5 i, u = - 5 i

u = 1, u = - 1, u = 5 i, u = - 5 i

Setze

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

löse für

x

Löse

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

Löse

x^{2} = - 1 : x = i, x = - i

Löse

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

Löse

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

Die Lösungen sind

x = 1, x = - 1, x = i, x = - i, x = \frac{5}{2} + \frac{5}{2} i, x = - \frac{5}{2} - \frac{5}{2} i, x = \frac{5}{2} - \frac{5}{2} i, x = - \frac{5}{2} + \frac{5}{2} i

Graph

Beliebte Beispiele

(1 + x)^{9} = 2

a^{3} = 3

solvefor y,x+y^3=27

so l v e f or y, x + y^{3} = 27

(x^2+3)^2+7x^2+21=-10

(x^{2} + 3)^{2} + 7 x^{2} + 21 = - 10

5 y (y - 4) (y - 7) = 0