Đáp án:1) x=4
2) $x = 5 + \sqrt {15} $
Giải thích các bước giải:
$\begin{array}{l}
b1:\,\sqrt {4x - 7} = 2x - 5\\
dkxd:\left\{ \begin{array}{l}
4x - 7 \ge 0\\
2x - 5 \ge 0
\end{array} \right. \Rightarrow x \ge \frac{5}{2}\\
pt \Leftrightarrow 4x - 7 = {\left( {2x - 5} \right)^2}\\
\Leftrightarrow 4x - 7 = 4{x^2} - 20x + 25\\
\Leftrightarrow 4{x^2} - 24x + 32 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 4\left( {tm} \right)\\
x = 2\left( {ktm} \right)
\end{array} \right.\\
Vay\,x = 4\\
b2:\sqrt {2x + 6} = x - 4\\
dkxd:\left\{ \begin{array}{l}
2x + 6 \ge 0\\
x - 4 \ge 0
\end{array} \right. \Rightarrow x \ge 4\\
pt \Rightarrow 2x + 6 = {\left( {x - 4} \right)^2}\\
\Rightarrow 2x + 6 = {x^2} - 8x + 16\\
\Rightarrow {x^2} - 10x + 10 = 0\\
\Rightarrow \left[ \begin{array}{l}
x = 5 - \sqrt {15} \left( {ktm} \right)\\
x = 5 + \sqrt {15} \left( {tm} \right)
\end{array} \right.\\
vay\,x = 5 + \sqrt {15}
\end{array}$
