Question

Aratati ca (1-2√6)² + (5+√3)(5-√3)+2(√2 +√3)² ∈ N

Answer 1

${(1 - 2 \sqrt{6}) }^{2} + ( 5+ \sqrt{3} )(5 - \sqrt{3} ) + 2 {( \sqrt{2} + \sqrt{3}) }^{2} \\ 1 - 4 \sqrt{6} + 24 + 25 - 3 + 2(2 + 2 \sqrt{6} + 3) \\ 1 - 4 \sqrt{6} + 24 + 25 - 3 + 2(5 + 2 \sqrt{6} ) \\ 1 - 4 \sqrt{6} + 24 + 25 - 3 + 10 + 4 \sqrt{6}$
4 rad din 6 se simplifica
Aduni/Scazi ce ramane
$1 + 24 + 25 - 3 + 10 = 57$
57 este nr natural.