ĐKXĐ: \(\left\{{}\begin{matrix}x\ge0\\\sqrt{x}-2\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ne4\end{matrix}\right.\)
\(P=\dfrac{\sqrt{x}+7}{\sqrt{x}-2}=\dfrac{\sqrt{x}-2+9}{\sqrt{x}-2}=\dfrac{\sqrt{x}-2}{\sqrt{x}-2}+\dfrac{9}{\sqrt{x}-2}=1+\dfrac{9}{\sqrt{x}-2}\)
\(\left|P\right|=2\Rightarrow\left|1+\dfrac{9}{\sqrt{x}-2}\right|=2\)
\(\Rightarrow\left[{}\begin{matrix}1+\dfrac{9}{\sqrt{x}-2}=2\\1+\dfrac{9}{\sqrt{x}-2}=-2\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}\dfrac{9}{\sqrt{x}-2}=1\\\dfrac{9}{\sqrt{x}-2}=-3\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{x}-2=9\\-3\left(\sqrt{x}-2\right)=9\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=11\\\sqrt{x}=-1\left(ktm\right)\end{matrix}\right.\\ \Leftrightarrow x=121\left(tm\right)\)
