Đáp án:
\[x = 5\]
Giải thích các bước giải:
ĐKXĐ: \(x \ge \frac{3}{2}\)
Ta có:
\(\begin{array}{l}
\sqrt {x + 2} + 2x - 10 = \sqrt {2x - 3} \\
\Leftrightarrow \sqrt {x + 2} - \sqrt {2x - 3} + 2x - 10 = 0\\
\Leftrightarrow \frac{{x + 2 - 2x + 3}}{{\sqrt {x + 2} + \sqrt {2x - 3} }} + 2\left( {x - 5} \right) = 0\\
\Leftrightarrow \frac{{5 - x}}{{\sqrt {x + 2} + \sqrt {2x - 3} }} + 2\left( {x - 5} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 5 = 0\\
\frac{1}{{\sqrt {x + 2} + \sqrt {2x - 3} }} = 2
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 5\\
\sqrt {x + 2} + \sqrt {2x - 3} = \frac{1}{2}
\end{array} \right.\\
x \ge \frac{3}{2} \Rightarrow \sqrt {x + 2} \ge \sqrt {\frac{7}{2}} > \frac{1}{2} \Rightarrow \sqrt {x + 2} + \sqrt {2x - 3} > \frac{1}{2},\,\,\,\,\forall x\\
\Rightarrow x = 5
\end{array}\)
