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Beliebt Algebra >

x^3+2+x=0

Lösung

x^{3} + 2 + x = 0

Lösung

x = - 1, x = \frac{1}{2} + i \frac{7}{2}, x = \frac{1}{2} - i \frac{7}{2}

Schritte zur Lösung

x^{3} + 2 + x = 0

Schreibe in der Standard Form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{3} + x + 2 = 0

Faktorisiere

x^{3} + x + 2 : (x + 1) (x^{2} - x + 2)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 1 = 0 : x = - 1

Löse

x^{2} - x + 2 = 0 : x = \frac{1}{2} + i \frac{7}{2}, x = \frac{1}{2} - i \frac{7}{2}

Die Lösungen sind

x = - 1, x = \frac{1}{2} + i \frac{7}{2}, x = \frac{1}{2} - i \frac{7}{2}

Graph

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