[tex]\frac{3-\sqrt7}{3+\sqrt7}+\frac{3+\sqrt7}{3-\sqrt7}=\frac{(3-\sqrt7)(3-\sqrt7)}{(3+\sqrt7)(3-\sqrt7)}+\frac{(3+\sqrt7)(3+\sqrt7)}{(3-\sqrt7)(3+\sqrt7)}=\\
\frac{9-2\sqrt7+7}{2}+\frac{9+2\sqrt7+7}{2}=\frac{9-2\sqrt7+7+9+2\sqrt7+7}{2}=\\
\frac{32}{2}=16\in\mathbb{N}[/tex]
Cred ca se cerea sa arati ca numarul e natural sau rational, ca real e cu certitudine, nu trebuie demonstrat!
