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Beliebt Algebra >

x^3+2x^2+2x+1=0

Lösung

x^{3} + 2 x^{2} + 2 x + 1 = 0

Lösung

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

Schritte zur Lösung

x^{3} + 2 x^{2} + 2 x + 1 = 0

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 1 = 0 : x = - 1

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

(2 x + 1)^{3} = 100

x^{3} - x^{2} + 2 x - 1 = 0

x^{3} + 4 x^{2} = 360

4x^4-32x^2+48=0

4 x^{4} - 32 x^{2} + 48 = 0

(x-2)^4=(x-2)^2

(x - 2)^{4} = (x - 2)^{2}