已知X,Y满足Y^2=2X+6Y-X^2-10,求代数式XY/X+Y的值

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已知X,Y满足Y^2=2X+6Y-X^2-10,求代数式XY/X+Y的值
已知X,Y满足Y^2=2X+6Y-X^2-10,求代数式XY/X+Y的值

已知X,Y满足Y^2=2X+6Y-X^2-10,求代数式XY/X+Y的值
y2=2x+6y-x2-10
移项：
x2+y2-2x-6y+10=0
整理得：
x2-2x+1+y2-6y+9=0
即：
(x-1)2+(y-3)2=0
平方和等于0,则各项等于0,
因此 x-1=0 y-3=0
所以 x=1 y=3
所以 xy/（x+y）=3/4

Y^2=2X+6Y-X^2-10,
整理得
y^2-6y+9=-(x^2-2x+1)
(y-3)^2+(x-1)^2=0
所以 y=3 x=1
XY/X+Y
=3/4

通过整理得：（x-1）^2 + (y-3)^2 = 0
解得x= 1,y=3
既xy = 3,x+y=4
可知：XY/X+Y=3/4

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