3a+2b=2,求(2/a+1/(3b))的最小值
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![3a+2b=2,求(2/a+1/(3b))的最小值](/uploads/image/z/7208388-36-8.jpg?t=3a%2B2b%3D2%2C%E6%B1%82%EF%BC%882%2Fa%2B1%2F%283b%29%EF%BC%89%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC)
3a+2b=2,求(2/a+1/(3b))的最小值
3a+2b=2,求(2/a+1/(3b))的最小值
3a+2b=2,求(2/a+1/(3b))的最小值
2(2/a+1/3b)
=(3a+2b)(2/a+1/3b)
=6+a/b+4b/a+2/3
=20/3+(a/b+4b/a)
a/b+4b/a≥2√(a/b*4b/a)=4
则2(2/a+1/3b)≥20/3+4=32/3
2/a+1/3b≥16/3
最小值是16/3