答：
xy>0,則x和y同號(hào)
3x+y=xy>0
所以：x和y都是正數(shù)
3x=(x-1)y
y=3x/(x-1)=3(x-1+1)/(x-1)=3+3/(x-1)>3
所以：x>1,y>3
x+y
=x+3x/(x-1)
=(x^2-x+3x)/(x-1)
=(x^2+2x)/(x-1)
=[(x-1)^2+4(x-1)+3]/(x-1)
=(x-1)+3/(x-1)+4
>=2√3+4
當(dāng)且僅當(dāng)x-1=3/(x-1)即x-1=√3,x=1+√3時(shí)取得最小值2√3+4
所以：x+y的最小值為2√3+4