矩形的周长是16cm,它的两边x,y是整数,且满足x2-2xy+y2-x+y-2=0,求矩形的面积.

问题描述:

矩形的周长是16cm,它的两边x,y是整数,且满足x2-2xy+y2-x+y-2=0,求矩形的面积.

∵x2-2xy+y2-x+y-2=0,
∴x2-2xy+y2-(x-y)-2=0,
∴(x-y)2-(x-y)-2=0,
∴(x-y-1)2=0,
∴x-y-2=0,
∵x+y=

1
2
×16=8,
∴x=5,y=3,
∴矩形的面积=4×3=12(cm2).