de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

x^3=x^5+x^3+x

Lösung

x^{3} = x^{5} + x^{3} + x

Lösung

x = 0, x = - \frac{2}{2} + i \frac{2}{2}, x = - \frac{2}{2} - i \frac{2}{2}, x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2}{2} - i \frac{2}{2}

Schritte zur Lösung

x^{3} = x^{5} + x^{3} + x

Tausche die Seiten

x^{5} + x^{3} + x = x^{3}

Verschiebe

x^{3}

auf die linke Seite

x^{5} + x = 0

Faktorisiere

x^{5} + x : x (x^{2} + 2 x + 1) (x^{2} - 2 x + 1)

x (x^{2} + 2 x + 1) (x^{2} - 2 x + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x^{2} + 2 x + 1 = 0 or x^{2} - 2 x + 1 = 0

Löse

x^{2} + 2 x + 1 = 0 : x = - \frac{2}{2} + i \frac{2}{2}, x = - \frac{2}{2} - i \frac{2}{2}

Löse

x^{2} - 2 x + 1 = 0 : x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2}{2} - i \frac{2}{2}

Die Lösungen sind

x = 0, x = - \frac{2}{2} + i \frac{2}{2}, x = - \frac{2}{2} - i \frac{2}{2}, x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2}{2} - i \frac{2}{2}

Graph

Beliebte Beispiele

x^4-5x^3-15x^2+5x+14=0

x^{4} - 5 x^{3} - 15 x^{2} + 5 x + 14 = 0

solvefor x,x^3-3y^2+3y-1=0

so l v e f or x, x^{3} - 3 y^{2} + 3 y - 1 = 0

\frac{x ^{3} + 13}{2} = 20

2x^3+8x-4x-40=0

2 x^{3} + 8 x - 4 x - 40 = 0

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

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