c.
\(P=AB=\dfrac{7}{\sqrt{x}+8}.\dfrac{\sqrt{x}+8}{\sqrt{x}+3}=\dfrac{7}{\sqrt{x}+3}\)
Do \(\sqrt{x}\ge0\Rightarrow\sqrt{x}+3>0\Rightarrow P>0\)
Do \(\sqrt{x}+3\ge3\Rightarrow\dfrac{7}{\sqrt{x}+3}\le\dfrac{7}{3}\)
\(\Rightarrow0< P< \dfrac{7}{3}\)
Mà P là số nguyên nên \(\left[{}\begin{matrix}P=1\\P=2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{7}{\sqrt{x}+3}=1\\\dfrac{7}{\sqrt{x}+3}=2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\sqrt{x}+3=7\\\sqrt{x}+3=\dfrac{7}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{x}=4\\\sqrt{x}=\dfrac{1}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=16\\x=\dfrac{1}{4}\end{matrix}\right.\)
