Question

Aratati ca a=2×(8+radical din 18)-3×(4+radical din 8) este număr intreg cu ...

Answer 1

 

$\displaystyle\\a=2\times(8+\sqrt{18})-3\times(4+\sqrt{8})\\\\a=2\times8+2\times\sqrt{18}-3\times4-3\times\sqrt{8}\\\\a=16+2\times\sqrt{9\times2}-12-3\times\sqrt{4\times2}\\\\a=16+2\times3\sqrt{2}-12-3\times2\sqrt{2}\\\\a=16+6\sqrt{2}-12-6\sqrt{2}\\\\a=16-12+\underline{6\sqrt{2}}-\underline{6\sqrt{2}}\\\\a=16-12\\\\\boxed{\bf a=4\in Z}$