Question

Dau coroana!
Se considera expresia E(x)=(x+1)² + 2(x²+4x+3) + ( x+3) totul la a 2- a, unde x ∈ R. Demonstrati ca E(n) este patrat perfect, oricare ar fi numarul n

Answer 1

[tex]E(x)=(x+1)^2+2(x^2+4x+3)+(x+3)^2\\ E(x)=(x+1)^2+2(x^2+3x+x+3)+(x+3)^2\\ E(x)=(x+1)^2+2[x(x+3)+(x+3)]+(x+3)^2\\ E(x)=(x+1)^2+2(x+1)(x+3)+(x+3)^2\\ E(x)=(x+1+x+3)^2\\ E(n)=(2n+4)^2,\text{care este patrat perfect.}\\ [/tex]