Question

Aflati suma numerelor naturale x, pentru care fracţia $\frac{x^2+4}{x+2}$ ∈N

Answer 1

E(x) = (x^2 + 4)/(x+2) = (x^2 + 4x + 4 - 4x)/(x+2) = x+2 - 4x/(x+2)

E(x) =  x+2 - (4x + 8 - 8)/x+2) = x+2 - 4 + 8/(x+2)

E(x) = x-2 + 8/(x+2)

x+2 = 1,2,4,8

x+2 = 1  nu merge, x ∈ N

x+2 = 2, x=0

x+2 = 4, x=2

x+2 = 8, x=6

S=0+2+6 = 8