若X的平方减Y的平方减X加Y等于X减Y的差乘A,则A等于

x^2-y^2-x+y=(x-y)A(x-y)(x+y)-(x-y)=(x-y)A(x-y)(x+y-1)=(x-y)A(x-y)(x+y-1)-(x-y)A=0(x-y)(x+y-1-A)=0(x-y)=0或(x+y-1-A)=0x=y或A=x+y-1所以当x=y时,A为任意实数；或A=x+y-1