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Beliebt Algebra >

2x^4-9x^3-9x^2+81x-81=0

Lösung

2 x^{4} - 9 x^{3} - 9 x^{2} + 81 x - 81 = 0

Lösung

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

+1

Dezimale

x = - 3, x = 3, x = 1.5

Schritte zur Lösung

2 x^{4} - 9 x^{3} - 9 x^{2} + 81 x - 81 = 0

Faktorisiere

2 x^{4} - 9 x^{3} - 9 x^{2} + 81 x - 81 : (x + 3) (x - 3)^{2} (2 x - 3)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 3 = 0 : x = - 3

Löse

x - 3 = 0 : x = 3

Löse

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

Die Lösungen sind

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

Graph

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