正确答案应该是12or-12
(X+Y)*(X+Y)[1]=(A+B)*(A+B)[2],4XY[3]=52+4AB[4]
[1]-[3]=[2]-[4]
(X-Y)*(X-Y)=(A-B)*(A-B)-52
(A-B)*(A-B)-(X-Y)*(X-Y)=52
即(A-B-X+Y)*(A-B+X-Y)=52[5]
又因为X+Y=A+B,即A-X=Y-B,A-Y=X-B
则[5]变为2(A-X)*2(A-Y)=52
即(A-X)*(A-Y)=13,又已知X,Y,A,B都是正整数
且13为质数,所以A-X=1,A-Y=13或A-X=13,A-Y=1
则A-Y-(A-X)=X-Y=12或-12