X>0,Y>0,且1÷X+9÷Y=11/X+9/Y=1 ==>1/X=1-9/Y ==>X=Y/(Y-9)=1+9/(Y-9)所以X+Y=Y/(Y-9)+Y=1+9/(Y-9)+Y因为X>0,Y>0 ==>Y>9所以9/(Y-9)>0所以X+Y=1+9/(Y-9)+Y-9+9=10+9/(Y-9)+Y-9>=10+2√(9/(Y-9)*(Y-9))=16且当9/(Y-9)=(Y-9),有最小值
