Giải thích các bước giải:
ĐKXĐ: \(x \ge 1\)
Ta có:
\(\begin{array}{l}
3\sqrt {3x - 2} + 6\sqrt {x - 1} = 7x - 10 + 4\sqrt {3{x^2} - 5x + 2} \\
\Leftrightarrow 3\left( {\sqrt {3x - 2} - 2} \right) + 6\left( {\sqrt {x - 1} - 1} \right) = \left( {7x - 14} \right) + 4\left( {\sqrt {3{x^2} - 5x + 2} - 2} \right)\\
\Leftrightarrow 3.\frac{{3x - 6}}{{\sqrt {3x - 2} + 2}} + 6.\frac{{x - 2}}{{\sqrt {x - 1} + 1}} = 7\left( {x - 2} \right) + 4.\left( {\frac{{3{x^2} - 5x - 2}}{{\sqrt {3{x^2} - 5x + 2} + 2}}} \right)\\
\Leftrightarrow \left[ \begin{array}{l}
x = 2\\
\frac{9}{{\sqrt {3x - 2} + 2}} + \frac{6}{{\sqrt {x - 1} + 1}} = 7 + \frac{{4\left( {3x + 1} \right)}}{{\sqrt {3{x^2} - 5x + 2} + 2}}\,\,\,\,\,\,\left( 1 \right)
\end{array} \right.\\
\Leftrightarrow x = 2
\end{array}\)
