已知正实数x y满足x-根号xy-2y=0求 x+3根号xy+2y/2x-2根号下xy-y

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已知正实数x y满足x-根号xy-2y=0求 x+3根号xy+2y/2x-2根号下xy-y
已知正实数x y满足x-根号xy-2y=0求 x+3根号xy+2y/2x-2根号下xy-y

已知正实数x y满足x-根号xy-2y=0求 x+3根号xy+2y/2x-2根号下xy-y
答：
x>0,y>0
x-√(xy)-2y=0
(√x-2√y)(√x+√y)=0
因为：x>0,y>0
所以：√x+√y>0
所以：√x-2√y=0
所以：√x=2√y
所以：x=4y
所以：
[ x+3√(xy)+2y ] / [2x-2√(xy)-y ]
=(4y+3*2y+2y) / (8y-2*2y-y)
=12y / (3y)
=4

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