Răspuns:
Explicație pas cu pas:
E(x) =x( x²-4x+4)-x³+5x²-5x+1=
=x³-4x²+4x
-x³+5x²-5x+1 =
x²-x+1= x(x-1) +1= numar par (produs de 2 nr succesive) +1= numar imopar
E(-x) =x²+x+1
E(x) *E(-x) = (x²+1-x) (x²+1+x)= (x²+1)²-x²= x^4+2x²+1-x²=
=x^4+x²+1
x^4≥0
x²≥0
1=1
deci
E(x) *E(-x) ≥0+0+1=1, C.C.T.D.
