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Beliebt Algebra >

x(x-5)^3-14(x-5)^2=0

Lösung

x (x - 5)^{3} - 14 (x - 5)^{2} = 0

Lösung

x = 5, x = - 2, x = 7

Schritte zur Lösung

x (x - 5)^{3} - 14 (x - 5)^{2} = 0

Faktorisiere

x (x - 5)^{3} - 14 (x - 5)^{2} : (x - 5)^{2} (x + 2) (x - 7)

(x - 5)^{2} (x + 2) (x - 7) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 5 = 0 or x + 2 = 0 or x - 7 = 0

Löse

x - 5 = 0 : x = 5

Löse

x + 2 = 0 : x = - 2

Löse

x - 7 = 0 : x = 7

Die Lösungen sind

x = 5, x = - 2, x = 7

Graph

Beliebte Beispiele

4x(x-3)^2(2x-5)=0

4 x (x - 3)^{2} (2 x - 5) = 0

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

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

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

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

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

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