已知x大于0,y大于0,且x-6根号xy+8y=0,求2x+根号xy+y分之3x-根号xy-y
问题描述：
已知x大于0,y大于0,且x-6根号xy+8y=0,求2x+根号xy+y分之3x-根号xy-y
答
∵x大于0,y大于0,且x-6根号xy+8y=0
∴x-6根号xy+8y=0
(√x-2√y)(√x-4√y)=0
√x-2√y=0 √x-4√y=0
∴x1=4y x2=16y
∴x=4y 时
(3x-√xy-y)/(2x+√xy+y)
=（12y-2y-y)/(8y+2y+y)
=9y/(11y)
=9/11
x=16y 时
(3x-√xy-y)/(2x+√xy+y)
=（48y-4y-y)/(32y+4y+y)
=43y/(37y)
=43/37