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Beliebt Algebra >

27x^3-18x^2-3x+2=0

Lösung

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

Lösung

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

+1

Dezimale

x = 0.66666 \dots, x = - 0.33333 \dots, x = 0.33333 \dots

Schritte zur Lösung

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

Faktorisiere

27 x^{3} - 18 x^{2} - 3 x + 2 : (3 x - 2) (3 x + 1) (3 x - 1)

(3 x - 2) (3 x + 1) (3 x - 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

3 x - 2 = 0 or 3 x + 1 = 0 or 3 x - 1 = 0

Löse

3 x - 2 = 0 : x = \frac{2}{3}

Löse

3 x + 1 = 0 : x = - \frac{1}{3}

Löse

3 x - 1 = 0 : x = \frac{1}{3}

Die Lösungen sind

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

Graph

Beliebte Beispiele

4 x^{3} - 4 x^{2} + x = 0

x^{3} + 12 = 14

3 x^{3} - 12 x^{2} = 0

x^{3} + x = 7

\frac{1}{8} = z^{3}