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Beliebt Algebra >

x^5+x=0

Lösung

x^{5} + x = 0

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

x^{5} - 2 x + 1 = 0

m^{3} = - 1000

x^{4} - x = 1

4350=45000(1-k)^6

4350 = 45000 (1 - k)^{6}