设a>0,b>0,则(5a+1/3b)(3b+1/5a)的最小值是!

题目

设a>0,b>0,则(5a+1/3b)(3b+1/5a)的最小值是!

答案

(5a+1/3b)(3b+1/5a）=a^2+b^2+15ab+1/15ab
ab+1/ab>=2 当且仅当ab=1/ab即a^2b^2=1==>a^2=1 b^2=1
==>最小值=4