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文[1]第3题(4):已知正数a,b,c满足a+b+c=1,求证:1/a(1+b)+1/b(1+c)+1/c(1+a)的最小值是27/4.鉴于文[1]所给答案较为繁琐,笔者在此给出此题一种简洁证法,并将该结论做更一般性的推广.
(4): It is known that a, b and c satisfy a + b + c = 1, and prove that: 1 / a 1 + b 1 / b 1 + c 1 / The minimum value of c (1 + a) is 27/4. In view of the cumbersome answers given in [1], the author gives a concise proof of this problem and generalizes the conclusion.