Đáp án:a) $\left[ \begin{array}{l}
x = 10 + 2\sqrt 3 \\
x = - 2\sqrt 3 \\
x = 10 - 2\sqrt 3 \\
x = 2\sqrt 3
\end{array} \right.$
g) x=-1/3
Giải thích các bước giải:
$\begin{array}{l}
a){x^2} - 10x - 10\left| {x - 5} \right| + 38 = 0\\
\Leftrightarrow {x^2} - 10x + 25 - 10\left| {x - 5} \right| + 13 = 0\\
\Leftrightarrow {\left( {\left| {x - 5} \right|} \right)^2} - 10\left| {x - 5} \right| + 13 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\left| {x - 5} \right| = 5 + 2\sqrt 3 \\
\left| {x - 5} \right| = 5 - 2\sqrt 3
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 10 + 2\sqrt 3 \\
x = - 2\sqrt 3 \\
x = 10 - 2\sqrt 3 \\
x = 2\sqrt 3
\end{array} \right.\\
g)\left| {\left| {x - 2} \right| - x} \right| - \left| {x + 1} \right| = 2\\
\Rightarrow \left| {\left| {x - 2} \right| - x} \right| = \left| {x + 1} \right| + 2\\
\Rightarrow \left[ \begin{array}{l}
\left| {x - 2} \right| - x = \left| {x + 1} \right| + 2\\
- \left| {x - 2} \right| + x = \left| {x + 1} \right| + 2
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x - 2 - x = x + 1 + 2\left( {voi\,x \ge 2} \right)\\
2 - x - x = x + 1 + 2\left( {voi - 1 \le x < 2} \right)\\
2 - x - x = - x - 1 + 2\left( {voi\,x < - 1} \right)\\
x - 2 = \left| {x + 1} \right| + \left| {x - 2} \right|\left( 1 \right)
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = - 5\left( {loai} \right)\\
x = \frac{{ - 1}}{3}\left( {tm} \right)\\
x = 1\left( {loai} \right)\\
pt\left( 1 \right)vo\,nghiem
\end{array} \right. \Rightarrow x = \frac{{ - 1}}{3}\\
vayx = \frac{{ - 1}}{3}
\end{array}$
