Câu hỏi:

Ta có: $\overrightarrow{AM} = \frac{1}{2}(\overrightarrow{AD} + \overrightarrow{AC})$
$\overrightarrow{AM} = \frac{1}{2}\overrightarrow{AD} + \frac{1}{2}\overrightarrow{AC}$
$\overrightarrow{AE} = \frac{1}{3}\overrightarrow{AB} \Rightarrow \overrightarrow{AB} = 3\overrightarrow{AE}$
$\overrightarrow{AF} = \frac{2}{3}\overrightarrow{AC} \Rightarrow \overrightarrow{AC} = \frac{3}{2}\overrightarrow{AF}$
$\overrightarrow{AM} = \frac{1}{2}(3\overrightarrow{AE} - \overrightarrow{AD} + \frac{3}{2}\overrightarrow{AF}) = \frac{3}{2}\overrightarrow{AE} + \frac{3}{4}\overrightarrow{AF}$
Vậy $x = \frac{3}{2}$ và $y = \frac{3}{4}$
$x + y = \frac{3}{2} + \frac{3}{4} = \frac{9}{4}$