作CF⊥AB于F
CF∥DE,FE=BE
则AE-BE=AF+FE-BE=AF
则AE^2-BE^2=(AE+BE)(AE-BE)=AB(AE-BE)=AB*AF
又△ACF∽△ABC
AC/AF=AB/AC
AC^2=AF*AB
∴AE^2-BE^2=AC^2
作CF⊥AB于F
CF∥DE,FE=BE
则AE-BE=AF+FE-BE=AF
则AE^2-BE^2=(AE+BE)(AE-BE)=AB(AE-BE)=AB*AF
又△ACF∽△ABC
AC/AF=AB/AC
AC^2=AF*AB
∴AE^2-BE^2=AC^2