ĐKXĐ: \(x>0\)
\(\Leftrightarrow2\left(x+\frac{1}{4x}\right)-5\left(\sqrt{x}+\frac{1}{2\sqrt{x}}\right)+4=0\)
Đặt \(\sqrt{x}+\frac{1}{2\sqrt{x}}=a\ge\sqrt{2}\Rightarrow a^2=x+\frac{1}{4x}+1\Rightarrow x+\frac{1}{4x}=a^2-1\)
\(\Rightarrow2\left(a^2-1\right)-5a+4=0\Rightarrow2a^2-5a+2=0\)
\(\Rightarrow\left[{}\begin{matrix}a=2\\a=\frac{1}{2}\left(l\right)\end{matrix}\right.\) \(\Rightarrow\sqrt{x}+\frac{1}{2\sqrt{x}}=2\Rightarrow2x-4\sqrt{x}+1=0\)
\(\Rightarrow\sqrt{x}=\frac{2\pm\sqrt{2}}{2}\Rightarrow x=\frac{3\pm2\sqrt{2}}{2}\)
