Đáp án:
\(\begin{array}{l}
1)\,\,x = 4\\
2)\,\,\left[ \begin{array}{l}
x = \frac{{5 + \sqrt {21} }}{2}\\
x = \frac{{5 - \sqrt {21} }}{2}
\end{array} \right.
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
1)\,\,\left| {2 - 1} \right| = x - 3\\
\Leftrightarrow x - 3 = 1\\
\Leftrightarrow x = 1 + 3\\
\Leftrightarrow x = 4.\\
2)\,\,\left| {{x^2} - 4x + 5} \right| = x + 4\,\,\,\left( * \right)\\
Ta\,\,co:\,\,\,{x^2} - 4x + 5 = {x^2} - 4x + 4 + 1 = {\left( {x - 2} \right)^2} + 1 > 0\,\,\,\forall x\\
\Rightarrow \left( * \right) \Leftrightarrow {x^2} - 4x + 5 = x + 4\\
\Leftrightarrow {x^2} - 5x + 1 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{{5 + \sqrt {21} }}{2}\\
x = \frac{{5 - \sqrt {21} }}{2}
\end{array} \right..
\end{array}\)
