2.1) \(A=\dfrac{\sqrt{x}+7}{\sqrt{x}+2}=1+\dfrac{5}{\sqrt{x}+2}>1\)
Ta có \(\sqrt{x}+2\ge2\Rightarrow\dfrac{5}{\sqrt{x}+2}\le\dfrac{5}{2}< 3\Rightarrow A< 4\)
mà \(A\in Z\Rightarrow\left[{}\begin{matrix}A=2\\A=3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\dfrac{5}{\sqrt{x}+2}=1\\\dfrac{5}{\sqrt{x}+2}=2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\sqrt{x}+2=5\\\sqrt{x}+2=\dfrac{5}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=9\\x=\dfrac{1}{4}\end{matrix}\right.\)