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Se considera E(x)=(2x²+x+1)(2x²+x+3)+1. Aratati ca E(x) poate fi scris ca patrat perfect.

Răspuns :

E(x) = (2x²+x+1)(2x²+x+3)+1

E(x) = (2x²+x+1)[(2x²+x+1)+2]+1

E(x) = (2x²+x+1)(2x²+x+1)+2(2x²+x+1)+1

E(x) = (2x²+x+1)²+2(2x²+x+1)+1

E(x) = [(2x²+x+1)+1]²

E(x) = (2x²+x+2)²