若a>0,b>0,且a+b=4,3/a+2/b的最小值是
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![若a>0,b>0,且a+b=4,3/a+2/b的最小值是](/uploads/image/z/3786944-32-4.jpg?t=%E8%8B%A5a%3E0%2Cb%3E0%2C%E4%B8%94a%2Bb%3D4%2C3%2Fa%2B2%2Fb%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E6%98%AF)
若a>0,b>0,且a+b=4,3/a+2/b的最小值是
若a>0,b>0,且a+b=4,3/a+2/b的最小值是
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