左式=ab+a/b+1/ab+b/a =(a2b2+a2+1+b2)/ab =[a2b2+(1-2ab)+1]/ab =[(ab-1)2+1]/ab a+b=1 ab≤[(a+b)/2]²=1/4 所以(ab-1)^2+1≥25/16,0相乘得到，左式≥25/4
