Đáp án:
\({m = 3;\,\,m = \frac{{21 \pm 3\sqrt 5 }}{2}}\)
Giải thích các bước giải:
\(\begin{array}{l}
\Rightarrow \left\{ \begin{array}{l}
{a^2} - ma + 2 = 0\\
{\left( {3 - a} \right)^2} + 2\left( {3 - a} \right) - m = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
{a^2} - ma + 2 = 0\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\\
{a^2} - 8a + 15 - m = 0\,\,\left( 2 \right)
\end{array} \right.\\
\Leftrightarrow \left( {m - 8} \right)a + 13 - m = 0\\
+ )\,\,m = 8 \Leftrightarrow 0a + 5 = 0\,\,\left( {Vo\,\,li} \right)\\
+ )\,\,m \ne 8 \Rightarrow a = \frac{{m - 13}}{{m - 8}}\\
Thay\,\,vao\,\,\left( 1 \right)\\
\Rightarrow {\left( {\frac{{m - 13}}{{m - 8}}} \right)^2} - m.\frac{{m - 13}}{{m - 8}} + 2 = 0\\
\Leftrightarrow {\left( {m - 13} \right)^2} - m\left( {m - 13} \right)\left( {m - 8} \right) + 2{\left( {m - 8} \right)^2} = 0\\
\Leftrightarrow {m^2} - 26m + 169 - {m^3} + 21{m^2} - 104m + 2{m^2} - 32m + 128 = 0\\
\Leftrightarrow - {m^3} + 24{m^2} - 162m + 297 = 0\\
\Leftrightarrow {m^3} - 24{m^2} + 162m - 297 = 0\\
\Leftrightarrow \left( {m - 3} \right)\left( {{m^2} - 21m + 99} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
m = 3\\
m = \frac{{21 \pm 3\sqrt 5 }}{2}
\end{array} \right.\,\,\left( {tm} \right)
\end{array}\)
