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变形代换的目的是为了简化问题,暴露条件与结论间的本质联系,它往往来自朴实自然的想法,平凡中见神奇,以下以《数学通报》上就近刊登的一些数学问题的另解为例说明(考虑到篇幅,原先的解(证)均省略).例1(1575;2005(9))设a,b,c0,且a+2b+c=2.求证:3a+b+3b+c≥2(a+b)(b+c).分析欲
The purpose of transformational substitution is to simplify the essential connection between problems, exposure conditions and conclusions. It often comes from the simple and natural idea, which is magical in ordinary times. The following takes the solution of some mathematical problems recently published in the Mathematics Bulletin Example 1 (1575; 2005 (9)) Suppose a, b, c0, and a + 2b + c = 2. Prove that 3a + b + 3b + c ≧ 2 (a + b) (b + c)