由均值不等式 a+b≥2√ab
得：ab≤1/4
(a+1/a)(b+1/b)
=(a²+1)/a×(b²+1)/b
=(a²b²+a²+1+b²)/ab
=[a²b²+(a+b)²-2ab+1]/ab
=[a²b²+(1-2ab)+1]/ab
=[(ab-1)²+1]/ab
(ab-1)²+1≥25/16
∵ 0
由均值不等式 a+b≥2√ab
得：ab≤1/4
(a+1/a)(b+1/b)
=(a²+1)/a×(b²+1)/b
=(a²b²+a²+1+b²)/ab
=[a²b²+(a+b)²-2ab+1]/ab
=[a²b²+(1-2ab)+1]/ab
=[(ab-1)²+1]/ab
(ab-1)²+1≥25/16
∵ 0