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本刊1987年第二期P39上给出了一种用二元均值不等式证明三元均值不等式的巧妙证法。它与教学参考书中给出的证法,就证明的基本思路来说完全类似(都是通过“添项”,使奇数项的和变为偶数项的和,从而使二元均值不等式的应用成为可能),只不过添凑的项不同而已(一个添加三个正数的几何平均数,另一个添加三个正数的算术平均数)。这种采用“添项”思想的证明方法,技巧性较强,学生难以想到。在下面笔者给出的新的证明中,除了注意到恒等
In the second issue of P39 in 1987, an ingenious method to prove a ternary mean inequality using a bivariate inequality is given. It is similar to the proof given in the teaching reference book and is based on the basic idea of the proof (it is through “adding items”) that the sum of odd items becomes the sum of even items, so that the application of the bivariate mean inequality It’s possible), but it’s just a matter of adding different items (a geometric mean with three positive numbers added, and an arithmetic average with three positive numbers added). This method of proof using the “adding item” idea is more technical and difficult for students to think of. In the new proof given by the author below, in addition to the attention to equality