Question

E(x)=(x+2)(x"+4x+4)-x-2 totul supra x(x+5)+6
x"= x la puterea a doua
a) Aratati ca E(n) apartine N
N- numere naturale

Answer 1

E(x)=$\frac{(x+2)( x^{2} 4x+4)-(x+2)}{ x^{2} +5x+6}= \frac{(x+2)( x^{2} +4x+3)}{(x+2)(x+3)}= \frac{(x+2)(x+1)(x+3)}{(x+2)(x+3)} =x+1$, care apartine lui N pentru orice x∈N.