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题设a,b,c是正实数,且满足abc=1,求证:(a-1+1/b)(b-1+1/c)(c-1+1/a)≤1. 这是第41届国际数学奥林匹克竞赛试题第2题,现提供一种简捷新颖的证法.供同学们参考.
The question is that a, b, c are positive real numbers, and satisfies abc=1. Proof: (a-1+1/b)(b-1+1/c)(c-1+1/a)≤1. This is The second question of the 41st International Mathematical Olympiad Test Questions is to provide a simple and novel proof method for students’ reference.