ĐKXĐ: \(x\ge\frac{5}{4}\)
\(pt\Leftrightarrow4x^2-12x+8=2\sqrt{4x-5}\)
\(\Leftrightarrow4x^2-8x+4=4x-5+2\sqrt{4x-5}+1\)
\(\Leftrightarrow4\left(x-1\right)^2=\left(\sqrt{4x-5}+1\right)^2\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{4x-5}+1=2x-2\\\sqrt{4x-5}+1=2-2x\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{4x-5}=2x-3\left(1\right)\\\sqrt{4x-5}=1-2x\left(2\right)\end{matrix}\right.\)
Vì \(x\ge\frac{5}{4}\Rightarrow\sqrt{4x-5}=1-2x\le-4\)
\(\Rightarrow\) Phương trình \(\left(2\right)\) vô nghiệm
\(\left(1\right)\Leftrightarrow\left\{{}\begin{matrix}4x-5=\left(2x-3\right)^2\\2x-3\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x-5=4x^2+9-12x\\x\ge\frac{3}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x^2-16x+14=0\\x\ge\frac{3}{2}\end{matrix}\right.\)
\(\Leftrightarrow x=\frac{4+\sqrt{2}}{2}\left(tm\right)\)
