\(\begin{array}{l}
y' = {x^2} - 2\left( {m + 2} \right)x + {m^2} + 4m + 3\\
\Delta ' = {\left( {m + 2} \right)^2} - \left( {{m^2} + 4m + 3} \right) = 1 > 0\\
\Rightarrow y' = 0 \Leftrightarrow \left[ \begin{array}{l}
x = m + 1\\
x = m + 3
\end{array} \right.\\
\Rightarrow {x_1} = m + 1;{x_2} = m + 3\\
x_1^2 = {x_2} \Leftrightarrow {\left( {m + 1} \right)^2} = m + 3\\
\Leftrightarrow {m^2} + m - 2 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
m = 1\\
m = - 2
\end{array} \right.
\end{array}\)
