Question

Ajutor,va rog..
Fie expresia E(x)=(x²+2x)(x²+2x+2)+1
Sa se descompuna E(x).Este aceasta patrat perfect?

Answer 1

E(x)=(x²+2x)[(x²+2x)+2]+1=(x²+2x)²+2(x²+2x)+1=[(x²+2x)+1]²=(x²+2x+1)²=

$=((x+1)^2)^2=(x+1)^4$

Answer 2

E(x)=(x²+2x)[(x²+2x)+2]+1=(x²+2x)²+2(x²+2x)+1=[(x²+2x)+1]²=(x²+2x+1)²=[(x+1)²]² deci este patrat perfect