由均值不等式 a+b≥2√ab ab≤1/4 证法一 (a+1/a)(b+1/b) =(a^2+1)/a*(b^2+1)/b =(a^2b^2+a^2+1+b^2)/ab =[a^2b^2+(a+b)^2-2ab+1]/ab =[a^2b^2+(1-2ab)+1]/ab =[(ab-1)^2+1]/ab (ab-1)^2+1≥25/16 0