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Beliebt Algebra >

x^5+x^3+x=0

Lösung

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

Lösung

x = 0, x = \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} - \frac{3}{2} i, x = - \frac{1}{2} + \frac{3}{2} i

Schritte zur Lösung

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

Faktorisiere

x^{5} + x^{3} + x : x (x^{4} + x^{2} + 1)

x (x^{4} + x^{2} + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x^{4} + x^{2} + 1 = 0

Löse

x^{4} + x^{2} + 1 = 0 : x = \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} - \frac{3}{2} i, x = - \frac{1}{2} + \frac{3}{2} i

Die Lösungen sind

x = 0, x = \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} - \frac{3}{2} i, x = - \frac{1}{2} + \frac{3}{2} i

Graph

Beliebte Beispiele

x^3-3x^2+6x-18=0

x^{3} - 3 x^{2} + 6 x - 18 = 0

z^{4} - 5 z^{2} + 4 = 0

s (s + 1) (s + 2) = 0

s^{3} = 91.125

2 = x^{25}