Punctul a)
[tex] E(x) = (3x+1)^2 -(2x-1)(2-x) -(2x-3)(2x+3) + \\ + x(3-6x)-8 \\ E(x) = 9x^2 +6x+1-(5x-2x^2-2) - \\ -4x^2 +9 +3x-6x^2 -8 \\ E(x) = -x^2 +9x +2 -5x+2x^2 +2 \\ E(x) = x^2 +4x +4 \\ \tt E(x) =(x+2)^2 , \ \forall x\in \mathbb{R} [/tex]
Punctul b)
[tex] k=E(\sqrt{2}) -E(-\sqrt{2}) \\ k = (\sqrt{2} +2)^2 -(2-\sqrt{2})^2 \\ k= 2+4\sqrt{2} +4 -(4-4\sqrt{2} +2) \\ k=6+4\sqrt{2} -6+4\sqrt{2} \\ \tt k=8\sqrt{2} \ \in \mathbb{R} - \mathbb{Q} [/tex]
