x(x+1)(x+2) - x(x+1) = 180
x(x+1)[(x+2) -1] = 180
x(x+1)[x+2 -1] = 180
x(x+1)(x+1) = 180
x(x+1)^2 = 180
x(x^2 +2x+1)= 180
x^3 +2x^2+x= 180
x^3 + 2x^2 + x - 180 = 0
Cautam printre divizorii lui 180 si
observam ca 5 este solutie a ecuatiei.
x^3 - 5x^2 + 5x^2 + 2x^2 + x - 180 = 0
x^3 - 5x^2 + 7x^2 + x - 180 = 0
x^3 - 5x^2 + 7x^2 -35x + 35x + x - 180 = 0
(x^3 - 5x^2) + (7x^2 -35x) + (36x - 180) = 0
x^2(x-5) + 7x(x - 5)+ 36(x - 5) = 0
(x - 5)(x^2 + 7x + 36) = 0
x^2 + 7x + 36 = 0 nu are solutii reale.
x - 5 = 0
x = 5
Solutia problemei:
Primul numar = x = 5
Al doilea numar = x + 1 = 5+1 = 6
Al treilea numar = x + 2 = 5 + 2 = 7
Verificare:
5 × 6 = 30
5 × 6 × 7 = 210
210 - 30 = 180
