Đáp án:
$S = \left\{ {4;\,\,5} \right\}.$
Giải thích các bước giải:
$\begin{array}{l}
\sqrt {x - 4} \left( {{x^2} - 6x + 5} \right) = 0\,\,\,\,\,\left( * \right)\\
DK:\,\,\,x \ge 4\\
\left( * \right) \Leftrightarrow \left[ \begin{array}{l}
\sqrt {x - 4} = 0\\
{x^2} - 6x + 5 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x - 4 = 0\\
\left( {x - 1} \right)\left( {x - 5} \right) = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 4\,\,\,\left( {tm} \right)\\
x = 1\,\,\,\left( {ktm} \right)\\
x = 5\,\,\,\left( {tm} \right)
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x = 4\\
x = 5
\end{array} \right..
\end{array}$
Vậy $S = \left\{ {4;\,\,5} \right\}.$
