(a+1/a)(b+1/b) ab+b/a+a/b+1/(ab) =(a²b²+b²+a²+1)/(ab) =[a²b²+(1-2ab)+1]/(ab) =[(ab-1)²+1]/(ab) ∵a+b=1 ∴ab≤[(a+b)/2]²=1/4 ∴(ab-1)²+1≥25/16,0