$\begin{array}{l}
1/A\,la\,tap\,rong\, \Leftrightarrow pt\,{x^2} - 2\left( {m - 2} \right)x + {m^2} - m + 9 = 0\,vo\,nghiem\\
\Leftrightarrow \Delta ' = {\left( {m - 2} \right)^2} - {m^2} + m - 9 < 0 \Leftrightarrow {m^2} - 4m + 4 - {m^2} + m - 9 < 0\\
\Leftrightarrow - 3m - 5 < 0 \Leftrightarrow m > - \frac{5}{3}\\
2/Goi\,M\,la\,trung\,diem\,BC\,ta\,co:\\
\left| {\overrightarrow {AB} + \overrightarrow {AC} } \right| = \left| {2\overrightarrow {AM} } \right| = 2\left| {\overrightarrow {AM} } \right| = 2AM = 2.AB\sin {60^0} = 2a.\frac{{\sqrt 3 }}{2} = a\sqrt 3
\end{array}$
