已知长方形的周长为20,它的两条邻边长x,y满足2(x-y)-x2+2xy-y2-1=0,求此长方形的 面积

2(x-y) - (x^2 - 2xy + y^2) - 1 = 0
即
-2(x-y) + (x-y)^2 +1 = 0
(x-y-1)^2 = 0
x-y -1 = 0
x-y = 1 (1)
长方形周长为20,即2x+2y = 20,x+y=10 (2)
解(1)(2)组成的二元一次方程组得
x=11/2
y=9/2
长方形面积=x*y = 99/4