3. In $\triangle A B C$, if $A B=A C, \angle B A C=$ $120^{\circ}, D$ is the midpoint of side $B C$, and $D E \perp A B$ at $E$. Then $A E: B D=$
3.
$1: 2 \sqrt{3}$ (Hint: Connect $A D$, then $A D \perp B C$. )