∵ABCD是平行四边形, ∴AD∥CF, ∴CG/DG=GF/AG,
∴(DC-DG)/DG=2/(AE+EG)=2/[AE+(EF-GF)]=2/[AE+(3-2)],
∴DC/DG-1=2/(AE+1), ∴DC/DG=1+2/(AE+1)=(AE+3)/(AE+1).······①
∵ABCD是平行四边形, ∴DG∥AB、DC=AB, ∴△DGE∽△BAE,
∴DG/AB=EG/AE, ∴DG/DC=(EF-GF)/AE=(3-2)/AE=1/AE.······②
①×②,得:1=(AE+3)/[AE(AE+1)], ∴AE(AE+1)=AE+3, ∴AE^2=3,
∴AE=√3.