\(ĐK:x\ge\frac{5}{2}\)
\(3\sqrt{2x-1}=2x-5\Leftrightarrow18x-9=4x^2-10x+25\Leftrightarrow4x^2-28x+34=0\Leftrightarrow x^2-7x+\frac{17}{2}=0\Leftrightarrow x^2-2.\frac{7}{2}x+\frac{49}{4}-\frac{15}{4}=0\Leftrightarrow\left(x-\frac{7}{2}\right)^2=\frac{15}{4}\Leftrightarrow\left[{}\begin{matrix}x-\frac{7}{2}=\frac{\sqrt{15}}{2}\\x-\frac{7}{2}=\frac{-\sqrt{15}}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{\sqrt{15}+7}{2}\left(thoaman\right)\\x=\frac{-\sqrt{15}+7}{2}\left(loai\right)\end{matrix}\right.\Rightarrow x=\frac{\sqrt{15}+7}{2}\)
DKXĐ : .............
\(=>\left(3\sqrt{2x-1}\right)^2=\left(2x-5\right)^2\)
=> \(9\left(2x-1\right)=4x^2-10x+25\)
=> \(18x-9=4x^2-10x+25\)
=> \(18x-9-4x^2+20x-25=0\)
=> \(38x-34-4x^2=0\)
=> \(-4x^2+38x-34=0\)
