在△ABC中,点D、E分别在AB、AC边上,∠ADE=∠C,BD=AE+AD,CE=AE-AD,求BC：DE的值

∠ADE=∠C;∠A=∠A;==>△ABC∽△AED==>AC/AD=AB/AE=BC/DE;==>(AC+AB)/(AD+AE)=(AB-AC)/(AE-AD)=BC/DE;∵BD=AE+AD,CE=AE-AD;∴AC+AB/BD=AB-AC/CE=BC/DE;==>(AD+BD+AE+CE)/BD=(AD+BD-AE-EC)/CE=BC/DE;==>(2BD+CE)/BD=(BD-2CE)/CE=BC/DE;==>BD^2-4BD*CE-CE^2=0;==>BD=(2+根号5)CE;==>BC/DE=(BD-2CE)/CE=[(2+根号5)CE-2CE]/CE=根号5;BC：DE的值 为根号5;