Question

Aratati ca numarul b=(x^2+x+1)(x^2+x+3)+1 este patrat perfect.

Answer 1

(x²+x+1)(x²+x+3)+1= [(x²+x+2)-1][(x²+x+2)+1]-1=(x²+x+2)²-1+1=(x²+x+2)²