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Beliebt Algebra >

x^9-x=0

Lösung

x^{9} - 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}, x = i, x = - i, x = - 1, x = 1

Schritte zur Lösung

x^{9} - x = 0

Faktorisiere

x^{9} - x : x (x^{2} + 2 x + 1) (x^{2} - 2 x + 1) (x^{2} + 1) (x + 1) (x - 1)

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

Löse

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

Löse

x + 1 = 0 : x = - 1

Löse

x - 1 = 0 : x = 1

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}, x = i, x = - i, x = - 1, x = 1

Graph

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