Răspuns:
2) a)
[tex]E(x) = (x+1)^2 - \blue{(-x-1)^2}+x^2+2x+1[/tex]
[tex]\blue{(-x-1)^2}=[(-1) \cdot(x+1)]^2=(-1)^2\cdot(x+1)^2=\bold{(x+1)^2}[/tex]
[tex]E(x) = (x+1)^2 -(x+1)^2+x^2+2x+1[/tex]
[tex]E(x) = x^2+2x+1[/tex]
[tex]\green{\bf E(x) = (x+1)^2}[/tex] → Adevarat
b)
[tex](x+1)^2\geq x[/tex]
[tex]x^2+2x+1\geq x[/tex]
x² ; x ; 1 - pozitiv > 0
2x > x
x² > x
2x > x ⇒ x² + 2x > x ⇒ x² + 2x + 1 > x → Adevarat
