(x+√3y)^2=21-12√3
x^2+3y^2+2√3xy=21-12√3
x^2+3y^2=21
2xy=-12
4x^2+12y^2=84
14xy=-84
两式相加
4x^2+14xy+12y^2=0
2x^2+7xy+6y^2=0
(2x+3y)(x+2y)=0
x=-3y/2或x=-2y
x=-2y代入2xy=-12解得y不为整数,舍去.
x=-3y/2代入2xy=-12
解得y=2 x=-3
x-y=-3-2=-5