de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

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

Lösung

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

Lösung

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = - 33, x = \frac{3 3}{2} - \frac{6 3 ^{5}}{2} i, x = \frac{3 3}{2} + \frac{6 3 ^{5}}{2} i

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} + 2 u - 3 = 0

Löse

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

u = 1, u = - 3

Setze

u = x^{3} w i e d er e in,

löse für

x

Löse

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

Löse

x^{3} = - 3 : x = - 33, x = \frac{3 3}{2} - \frac{6 3 ^{5}}{2} i, x = \frac{3 3}{2} + \frac{6 3 ^{5}}{2} i

Die Lösungen sind

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = - 33, x = \frac{3 3}{2} - \frac{6 3 ^{5}}{2} i, x = \frac{3 3}{2} + \frac{6 3 ^{5}}{2} i

Graph

Beliebte Beispiele

4x^3+30x^2+70x+50=0

4 x^{3} + 30 x^{2} + 70 x + 50 = 0

x^{4} + 8 = 0

x^3-15x^2+72x-108=0

x^{3} - 15 x^{2} + 72 x - 108 = 0

2 x^{3} + 16 x^{2} = 0

0.2x^3-0.2x^2-1.2x=0

0.2 x^{3} - 0.2 x^{2} - 1.2 x = 0