de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

x^8+4x^6-4x^2-1=0

Lösung

x^{8} + 4 x^{6} - 4 x^{2} - 1 = 0

Lösung

x = i, x = - i, x = 1, x = - 1, x = 2 - 3 i, x = - 2 - 3 i, x = 2 + 3 i, x = - 2 + 3 i

Schritte zur Lösung

x^{8} + 4 x^{6} - 4 x^{2} - 1 = 0

Schreibe die Gleichung um mit

u = x^{2}, u^{3} = x^{6}

und

u^{4} = x^{8}

u^{4} + 4 u^{3} - 4 u - 1 = 0

Löse

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

u = - 1, u = 1, u = - 2 + 3, u = - 2 - 3

Setze

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

löse für

x

Löse

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

Löse

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

Löse

x^{2} = - 2 + 3 : x = 2 - 3 i, x = - 2 - 3 i

Löse

x^{2} = - 2 - 3 : x = 2 + 3 i, x = - 2 + 3 i

Die Lösungen sind

x = i, x = - i, x = 1, x = - 1, x = 2 - 3 i, x = - 2 - 3 i, x = 2 + 3 i, x = - 2 + 3 i

Graph

Beliebte Beispiele

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

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

36 x^{3} - 100 x = 0

x^4+2x^3-2x-1=0

x^{4} + 2 x^{3} - 2 x - 1 = 0

x^{7} + 5 x^{3} + 6 = 0

2x^3+3x^2-8x-12=0

2 x^{3} + 3 x^{2} - 8 x - 12 = 0