Question

Aratati ca expresia ( x²+2x+2)(x²+2x+4)+1 este patrat perfect oricare ar fi x nr real.

Answer 1

$Notam~n=x^2+2x+2. \\ \\ (x^2+2x+2)(x^2+2x+4)+1= \\ \\ =n(n+2)+1= \\ \\ =n^2+2n+1= \\ \\ =(n+1)^2 -patrat~perfect$