Question

已知长方形周长为20,两边长分别为x,y (均为整数）且满足x-y-x^2+2xy-y^2+2=0,求长方形的面积

Answer 1

x-y-x^2+2xy-y^2+2=0

(x-y)-(x-y)^2+2=0

(x-y)^2-(x-y)-2=0

(x-y-2)(x-y+1)=0

x=2+y

x=y-1

2x+2y=20

4+2y+2y=20

y=4

x=6

面积s=24

2y-2+2y=20

y=5.5（舍去）