ĐK: \(x>0\)
\(PT\Leftrightarrow5\left(\sqrt{x}+\frac{1}{2\sqrt{x}}\right)-2\left(x+\frac{1}{4x}\right)-4=0\)
Đặt: \(\sqrt{x}+\frac{1}{2\sqrt{x}}=t\left(t>0\right)\) \(\Rightarrow t^2=x+\frac{1}{4x}+1\)
\(PT\Leftrightarrow5t-2\left(t^2-1\right)-4=0\)
\(\Leftrightarrow2t^2-5t+2=0\) \(\Rightarrow\left[{}\begin{matrix}t=2\\t=\frac{1}{2}\end{matrix}\right.\) (tm)
\(t=2\Rightarrow x+\frac{1}{4x}-3=0\Rightarrow x^2-3x+\frac{1}{4}\) \(=0\Rightarrow x=\frac{3\pm2\sqrt{2}}{2}\) (tm)
\(t=\frac{1}{2}\Rightarrow x+\frac{1}{4x}+\frac{3}{4}=0\) \(\Rightarrow x^2+\frac{3}{4}x+\frac{1}{4}=0\) (vô no)
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