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

E(x) = (x+1)^2 + 2(x^2+4x+3) + (x+3)^2 =
       = x^2 + 2x + 1 + 2x^2 + 8x + 6 + x^2 + 6x + 9 = 
       = 4x^2 + 16x + 16 = 
       = 4(x^2 + 4x + 4) = 
       = 2^2 (x+2)^2
Atunci putem spune ca E(n) este patratul perfect al lui 2(n+2)

Answer 2

E(x)=(x+1)²+2(x²+4x+3)+(x+3)²
E(x)=x²+2x+1+2x²+8x+6+x²+6x+9
E(x)=4x²+16x+16
E(x)=(2x+4)²⇒este patrat perfect