应该是:求证:(a+1/a)(b+1/b)>=25/4证明:(a+1/a)(b+1/b)=ab+a/b+1/ab+b/a =((ab)^2+a^2+1+b^2)/ab =[(ab)^2+(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左式≥25/4.
(a+1/a)>0(b+1/b)>0所以(a+1/a)(b+1/b)>=0
不规范的改革和