Question

Aratati ca numarul $N=(2- \sqrt{3} )^{2} +(3+ \sqrt{3} )^{2}-2 \sqrt{3}$ este natural.

Answer 1

$N=(2- \sqrt{3} )^{2} +(3+ \sqrt{3} )^{2}-2 \sqrt{3}= \\ =4-4\sqrt{3}+3+9+6\sqrt{3}+3-2\sqrt{3}= \\ = 4+3+9+3 -4\sqrt{3}+6\sqrt{3}-2\sqrt{3}= \\ =19 + 0\sqrt{3}= \\ =19 \\ cctd$