Question

Fie a= \frac{ \sqrt{7-4 \sqrt{3} } + \sqrt{4+2 \sqrt{3} }}{ x-2}.Valorile naturale ale lui x pentru care a∈Z sunt
Raspuns corect 1,3,5

Answer 1

$\displaystyle a= \frac{ \sqrt{7-4 \sqrt{3} } + \sqrt{4+2 \sqrt{3} }}{ x-2}=\\ \\ =\frac{\sqrt{(2-\sqrt3)^2}+\sqrt{(1+\sqrt3)^2}}{x-2}=\\ \\ \frac{2-\sqrt3+1+\sqrt3}{x-2}=\\ \\ =\frac 3{x-2}\\ \\ \\ a\in Z, ~pt~a\in[1,3,5]$