ĐKXĐ: \(\left\{{}\begin{matrix}x\ge0\\x\ne2\end{matrix}\right.\)
Đặt \(\sqrt{x}=a\ge0\)
\(\Leftrightarrow2a^2+5a>11+\frac{14}{a^2-2}\)
\(\Leftrightarrow a^2+5a+4+a^2-15+\frac{14}{a^2-2}>0\)
\(\Leftrightarrow a^2+5a+4+\frac{a^4-17a^2+16}{a^2-2}>0\)
\(\Leftrightarrow a^2+5a+4+\frac{\left(a^2+5a+4\right)\left(a^2-5a+4\right)}{a^2-2}>0\)
\(\Leftrightarrow1+\frac{a^2-5a+4}{a^2-2}>0\)
\(\Leftrightarrow\frac{2a^2-5a+2}{a^2-2}>0\Leftrightarrow\frac{\left(a-2\right)\left(2a-1\right)}{a^2-2}>0\)
\(\Rightarrow\left[{}\begin{matrix}a>2\\\frac{1}{2}< a< \sqrt{2}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x>4\\\frac{1}{4}< x< 2\end{matrix}\right.\)
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