Question

1.Demonstrati ca numerele m si n sunt patrate perfecte,unde :m=(x^2+2x)(x^2+2x+2)+1 si n=(4x^2+4x)(4x^2+4x-6)+9,oricare ar fi numarul natural x.

Answer 1

fie x²+2x=y
atunci m=y(y+2)+1=y²+2y+1=(y+1)², p.p.

fie 4x²+4x=z
atunci  n=z(z-6)+9=z(z-6)+9=z²-6z+9=(z-3)², p.p.
as simple as that!!!!