Đáp án:
\(\left[ \begin{array}{l}
m = 3\\
m = \frac{3}{2}
\end{array} \right..\)
Giải thích các bước giải:
\(\begin{array}{l}
\left( P \right):\,\,\,y = m{x^2} - 2mx - m - 2\,\,\,\,\,\left( {m \ne 0} \right)\\
d:\,\,\,y = 6x - 17\\
Phuong\,\,trinh\,\,hoanh\,\,do\,\,giao\,\,diem\,\,cua\,\,\,d\,\,va\,\,\left( P \right):\\
m{x^2} - 2mx - m - 2 = 6x - 17\\
\Leftrightarrow m{x^2} - 2\left( {m + 3} \right)x - m + 15 = 0\,\,\,\left( * \right)\\
\left( P \right)\,\,\,tiep\,\,xuc\,\,voi\,\,d\\
\Leftrightarrow \left( * \right)\,\,\,co\,\,nghiem\,\,kep\\
\Leftrightarrow \Delta ' = 0\\
\Leftrightarrow {\left( {m + 3} \right)^2} + m\left( {m - 15} \right) = 0\\
\Leftrightarrow {m^2} + 6m + 9 + {m^2} - 15m = 0\\
\Leftrightarrow 2{m^2} - 9m + 9 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
m = 3\,\,\,\left( {tm} \right)\\
m = \frac{3}{2}\,\,\,\left( {tm} \right)
\end{array} \right..
\end{array}\)
