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Beliebt Algebra >

x^3-6x+9=0

Lösung

x^{3} - 6 x + 9 = 0

Lösung

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

Schritte zur Lösung

x^{3} - 6 x + 9 = 0

Faktorisiere

x^{3} - 6 x + 9 : (x + 3) (x^{2} - 3 x + 3)

(x + 3) (x^{2} - 3 x + 3) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 3 = 0 or x^{2} - 3 x + 3 = 0

Löse

x + 3 = 0 : x = - 3

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

x^{3} + 2 x^{2} - 24 x = 0

5x^9-x^2+2x-3=7

5 x^{9} - x^{2} + 2 x - 3 = 7

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

x^{4} = x^{5}

(2 x + 1)^{3} = 900