Question

n=(√2+3) la puterea2+(√5-2)(√5+2)+1-6√2 este natural

Answer 1

$\displaystyle n=\left( \sqrt{2} +3 \right)^2+\left( \sqrt{5} -2 \right)\left( \sqrt{5} +2 \right)+1-6 \sqrt{2} \\ n=\left( \sqrt{2} \right)^2+2 \cdot \sqrt{2} \cdot 3+3^2+5-4+1-6 \sqrt{2} \\ n=2+6 \sqrt{2} +9+5-4+1-6 \sqrt{2} \\ n=13 \in N$