1/a+3/b=1
b+3a=ab
ab-3a-b=0
a(b-3)-(b-3)=3
(a-1)(b-3)=3
(a-1)(2b-6)=6
a>0,b>0
a-1>-1,2b-6>-6
所以,a-1>0,2b-6>0
(a-1)+(2b-6)>=2√[(a-1)(2b-6)]=2√6
a+2b>=7+2√6
a+2b的最小值为:7+2√6