Đáp án:
$x = - 2$
Giải thích các bước giải:
\[\begin{array}{l}
\overrightarrow {AM} = \frac{1}{2}\overrightarrow {AB} ,\overrightarrow {AN} = \frac{1}{4}\overrightarrow {AC} \\
\Rightarrow \overrightarrow {AM} - \overrightarrow {AN} = \frac{1}{2}\overrightarrow {AB} - \frac{1}{4}\overrightarrow {AC} \\
\Rightarrow \overrightarrow {NM} = \frac{1}{2}\overrightarrow {AB} - \frac{1}{4}\overrightarrow {AC} \\
Ma\,M,N,P\,thang\,hang\,nen\,x\overrightarrow {AB} + \overrightarrow {AC} = k\left( {\frac{1}{2}\overrightarrow {AB} - \frac{1}{4}\overrightarrow {AC} } \right)\\
\Leftrightarrow \left\{ \begin{array}{l}
x = \frac{k}{2}\\
1 = - \frac{k}{4}
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
k = 2x\\
1 = - \frac{{2x}}{4}
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
k = 2x\\
x = - 2
\end{array} \right. \Rightarrow x = - 2
\end{array}\]
