题目已知正数a,b,c满足2a+4b+7c≤2abc,求a+b+c的最小值.以上题目是2008年全国高中数学联赛吉林省预赛第17题,笔者在文[1]中给出了两种解答,更早的[2]和文[3]也各自给出了一种解答,遗憾的是,这四种解法都有一个同样的缺点,那就是,它们都是事先知道了最小值点后再求最小值的!如果事先不知道最小值点的话,以上四种解法都将无法找到配凑系数的方向 The problem is known a, b, c to meet 2a + 4b +7 c ≤ 2abc, seeking a + b + c minimum.The above topic is the 2008 National High School Math Jilin Province Preliminaries 17 questions, the author in the article [1] Two solutions are given, and earlier [2] and [3] each give an answer. Unfortunately, all four solutions have the same drawback, namely, they are known in advance After the minimum and then find the minimum value! If you do not know in advance the minimum point, the above four solutions will not find the direction of the cobbled coefficient