Question

aratati ca (-2 radical din 3+3 radical din 2)^2-(25-12 radical din 6) este natural

Answer 1

[tex](-2\sqrt3+3\sqrt2)^2-(25-12\sqrt6)\\ \text{Folosim: } (a-b)^2=a^2-2ab+b^2\\ 9\cdot2-2\cdot 2\sqrt3 \cdot 3\sqrt 2+4\cdot 3-25+12\sqrt 6=\\ 18-12\sqrt6 +12-25+12\sqrt6=18+12-25=\\ 35-25=5 \\ (-2\sqrt3+3\sqrt2)^2-(25-12\sqrt6) = 5\in \mathbb{N}[/tex]