若a,b c>0,abc =27则a+b+c的最小值

a-c-27/[(b-a)(b-c)]
换元:x=a-b;y=b-c则x,y>0
原式=x+y+27/(xy)>=2(xy)^0.5+27/(xy)=(xy)^0.5+(xy)^0.5+27/(xy)
>=3((xy)^0.5*(xy)^0.5*27/(xy))^(1/3)=9
当且仅当x=y;(xy