已知想x,y为正数,且根号x（根号x+根号Y）=3根号y（根号x+5根号y）,求x+根号xy-y分之2x+根号xy+3y的值

Question

已知想x,y为正数,且根号x（根号x+根号Y）=3根号y（根号x+5根号y）,求x+根号xy-y分之2x+根号xy+3y的值

Answer 1

√x(√x+√y)=3√y(√x+5√y),求：[2x+√(xy)+3y]/[x+√(xy)-y]=?
√x(√x+√y)=3√y(√x+5√y)
x+√(xy)=3√(xy)+15y
x-2√(xy)-15y=0
(√x+3√y)(√x-5√y)=0
x=y=0,或√x=5√y
1.当x=y=0,[2x+√(xy)+3y]/[x+√(xy)-y]无结果（无意义）；
2.当√x=5√y≠0时,
[2x+√(xy)+3y]/[x+√(xy)-y]
=[2*25|y|+5|y|+3y]/[25|y|+5|y|-y]
=[50y+5y+3y]/[25y+5y-y]
=58/29
=2