长方形的周长是16cm,它的两边x,y是整数,且满足x-y-x^2(x的二次方)+2xy-y^2+2=0,求面积.
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长方形的周长是16cm,它的两边x,y是整数,且满足x-y-x^2(x的二次方)+2xy-y^2+2=0,求面积.
长方形的周长是16cm,它的两边x,y是整数,且满足x-y-x^2(x的二次方)+2xy-y^2+2=0,求面积.
长方形的周长是16cm,它的两边x,y是整数,且满足x-y-x^2(x的二次方)+2xy-y^2+2=0,求面积.
x-y-x^2+2xy-y^2+2=0,
x^2+y^2-2xy=x-y+2,
(x-y)^2-(x-y)-2=0,
(x-y+1)(x-y-2)=0,
∴x-y+1=0...①或者x-y-2=0...②.,
又∵x+y=8;x,y是整数
∴②是对的,即x=5,y=3.
故 S=3*5=15.
x-y-x^2(x的二次方)+2xy-y^2+2=0
x-y+2-(x^2-2xy+y^2)=0
x-y+2-(x-y)^2=0
(x-y)^2-(x-y)-2=0
可解得x-y=2或-1
1)当x-y=2时
结合2(x+y)=16
求的x=5,y=3这样子面积=5*3=15
2)当x-y=-1时
结合2(x+y)=16
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x-y-x^2(x的二次方)+2xy-y^2+2=0
x-y+2-(x^2-2xy+y^2)=0
x-y+2-(x-y)^2=0
(x-y)^2-(x-y)-2=0
可解得x-y=2或-1
1)当x-y=2时
结合2(x+y)=16
求的x=5,y=3这样子面积=5*3=15
2)当x-y=-1时
结合2(x+y)=16
求的x=3.5,y=4.5不符合题目变长为正数,舍弃
所以,总之,面积=15
收起
x-y-x^2+2xy-y^2+2=0
(x-y)-(x-y)^2+2=0
(x-y)^2-(x-y)-2=
(x-y-2)(x-y+1)=0,
x-y-2=0,x-y+1=0
2(x+y)=16,x+y=8,x=5,y=3或x=3.5(不合题意,舍去)