Question

Expresia(x)=(x+1)la puterea a doua+ 2(xla puterea a doua+4x+3)+(x+3)totul la puterea a doua .Unde xinclus in multimea R.Demonstrati ca E(n) patrat perfect

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