[tex]\left\{{x\in \mathbb{N}|\,\sqrt{x^2-4} \in \mathbb{N}\right\} = \{2\}[/tex]
[tex]\\[/tex]
[tex]\sqrt{x^2-4}\text{ exista doar daca:}\\ \\ x^2-4\geq 0 \Rightarrow x^2 \geq 4 \Rightarrow |x|\geq 2 \Rightarrow \\ \\ \Rightarrow -2\geq x\quad \vee\quad x\geq 2\\\Rightarrow x \leq -2\quad \vee\quad x \geq 2\\ \\ \Rightarrow x\in (-\infty, -2]\cup[2+\infty)\cap \mathbb{N}\\ \\ \Rightarrow x\in \{2,3,4,5,6,7,...\}[/tex]
