x²y-2xy+y+x²-2x=1983
y(x²-2x+1)+x²-2x+1=1983+1
y(x-1)²+(x-1)²=1984
(y-1)(x-1)²=1984
因为1984=1984×1=496×4=124×16=31×64
所以① y-1=1984
(x-1)²=1
解得y=1985 x=0或2
②y-1=496
(x-1)²=4
解得y=497 x=3或-1
③y-1=124
(x-1)²=64
解得y=125 x=-7或9