Đáp án:
$\begin{array}{l}
1)3x.\left( {x - 5} \right) - 6\left( {5 - x} \right) = 0\\
\Rightarrow 3.x.\left( {x - 5} \right) + 6\left( {x - 5} \right) = 0\\
\Rightarrow \left( {x - 5} \right)\left( {3x + 6} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
x = 5\\
x = - 2
\end{array} \right.\\
Vậy\,x = 5;x = - 2
\end{array}$
2)
Ta có DE//BC nên theo Talet ta có:
$\begin{array}{l}
\dfrac{{AD}}{{AB}} = \dfrac{{AE}}{{AC}}\\
\Rightarrow AE = \dfrac{4}{6}.9 = 6\left( {cm} \right)\\
\Rightarrow CE = AC - AE = 9 - 6 = 3\left( {cm} \right)\\
3)\\
MN//BC\\
\Rightarrow \dfrac{{AM}}{{AB}} = \dfrac{{AN}}{{AC}} = \dfrac{{MN}}{{BC}}\\
\Rightarrow \dfrac{{16}}{{25}} = \dfrac{{10}}{{AC}} = \dfrac{{MN}}{{45}}\\
\Rightarrow \left\{ \begin{array}{l}
AC = \dfrac{{250}}{{16}} = \dfrac{{125}}{8}\left( {cm} \right)\\
MN = \dfrac{{16.45}}{{25}} = \dfrac{{144}}{5}\left( {cm} \right)
\end{array} \right.
\end{array}$
