\(\sqrt{10x+1}+\sqrt{3x-5}=\sqrt{9x+4}+\sqrt{2x-2}\left(ĐKXĐ:
x\ge\frac{5}{3}\right)\)
\(\Leftrightarrow\sqrt{10x+1}-\sqrt{9x+4}=\sqrt{2x-2}-\sqrt{3x-5}\)
\(\Leftrightarrow\frac{10x+1-\left(9x+4\right)}{\sqrt{10x+1}+\sqrt{9x+4}}=\frac{2x-2-\left(3x-5\right)}{\sqrt{2x-2}+\sqrt{3x-5}}\)
\(\Leftrightarrow\frac{x-3}{\sqrt{10x+1}+\sqrt{9x+4}}=\frac{3-x}{\sqrt{2x-2}+\sqrt{3x-5}}\)
\(\Leftrightarrow\left(x-3\right)\left(\frac{1}{\sqrt{10x+1}+\sqrt{9x+4}}+\frac{1}{\sqrt{2x-2}+\sqrt{3x-5}}\right)=0\)\(\Leftrightarrow\orbr{\begin{cases}x=3\\\sqrt{10x+1}+\sqrt{3x-5}+\sqrt{9x+4}+\sqrt{2x-2}=0\left(vo.nghiem\right)\end{cases}}\)
\(\Leftrightarrow x=3\)
