已知4x2+9y-4x-6y+2=0 求根号y/根号x+根号y - 根号y/根号x-根号y
问题描述：
已知4x2+9y-4x-6y+2=0 求根号y/根号x+根号y - 根号y/根号x-根号y
快.
答
因为4x^2+9y^2-4x-6y+2=0,
所以4x^2-4x+19y^2-6y+1=0,
(2x-1)^2+(3y-1)^2=0
所以2x-1=0,3y-1=0,
所以x=1/2.y=1/3
所以根号y/（根号x+根号y） - 根号y/（根号x-根号y ）
=√y/(√x+√y)-√y/(√x-√y)
=√y(√x-√y)/(x-y)-√y(√x+√y)/(x-y)
=(√xy-y-√xy-y)/(x-y)
=-2y/(x-y)
=-2*（1/3）/(1/2-1/3)
=(-2/3)/(1/6)
=-4