若a>0,b>0,且a+b=4,3/a+2/b的最小值是

问题描述:

若a>0,b>0,且a+b=4,3/a+2/b的最小值是

4(3/a+2/b)
=(a+b)·(3/a+2/b)
=3+2·a/b+3·b/a+2
=5+2·a/b+3·b/a
≥5+2√[2·a/b·3·b/a]
=5+2√6
∴3/a+2/b≥(5+2√6)/4