Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\sqrt {\dfrac{{2x - 3}}{{x - 1}}} = 2\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {\left[ \begin{array}{l}
x \ge \dfrac{3}{2}\\
x < 1
\end{array} \right.} \right)\\
\Leftrightarrow \dfrac{{2x - 3}}{{x - 1}} = 4\\
\Leftrightarrow 2x - 3 = 4.\left( {x - 1} \right)\\
\Leftrightarrow 2x - 3 = 4x - 4\\
\Leftrightarrow 4x - 2x = - 3 + 4\\
\Leftrightarrow 2x = 1\\
\Leftrightarrow x = \dfrac{1}{2}\,\,\,\,\left( {t/m} \right)\\
b,\\
\sqrt {4x - 12} + \sqrt {x - 3} = \dfrac{1}{3}\sqrt {9x - 27} + 4\,\,\,\,\,\,\,\,\,\,\,\left( {x \ge 3} \right)\\
\Leftrightarrow \sqrt {4.\left( {x - 3} \right)} + \sqrt {x - 3} = \dfrac{1}{3}.\sqrt {9.\left( {x - 3} \right)} + 4\\
\Leftrightarrow 2.\sqrt {x - 3} + \sqrt {x - 3} = \dfrac{1}{3}.3.\sqrt {x - 3} + 4\\
\Leftrightarrow 2\sqrt {x - 4} = 4\\
\Leftrightarrow \sqrt {x - 4} = 2\\
\Leftrightarrow x - 4 = 4\\
\Leftrightarrow x = 8\\
c,\\
2x - 3\sqrt {2x - 1} - 5 = 0\,\,\,\,\,\,\,\,\,\,\,\left( {x \ge \dfrac{1}{2}} \right)\\
\Leftrightarrow \left( {2x - 1} \right) - 3\sqrt {2x - 1} - 4 = 0\\
\Leftrightarrow \left[ {\left( {2x - 1} \right) - 4\sqrt {2x - 1} } \right] + \left[ {\sqrt {2x - 1} - 4} \right] = 0\\
\Leftrightarrow \sqrt {2x - 1} .\left( {\sqrt {2x - 1} - 4} \right) + \left( {\sqrt {2x - 1} - 4} \right) = 0\\
\Leftrightarrow \left( {\sqrt {2x - 1} - 4} \right)\left( {\sqrt {2x - 1} + 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sqrt {2x - 1} = 4\\
\sqrt {2x - 1} = - 1
\end{array} \right.\\
\Rightarrow \sqrt {2x - 1} = 4\\
\Leftrightarrow 2x - 1 = 16\\
\Leftrightarrow x = \dfrac{{17}}{2}
\end{array}\)
