Question

Answer 1

\(1,C=\dfrac{a+2\sqrt{a}+a-2\sqrt{a}}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\cdot\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}{2\sqrt{a}}=\dfrac{2a}{2\sqrt{a}}=\sqrt{a}\\ 2,C-2=\sqrt{a}-2< 0\Leftrightarrow0< a< 4\\ 3,\dfrac{4}{C+1}=\dfrac{4}{\sqrt{a}+1}\in Z\\ \Leftrightarrow\sqrt{a}+1\inƯ\left(4\right)=\left\{2;4\right\}\left(\sqrt{a}+1>1\right)\\ \Leftrightarrow\sqrt{a}\in\left\{1;3\right\}\\ \Leftrightarrow a\in\left\{1;9\right\}\left(tm\right)\)