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运用辩证的观点,可以将数学问题中一些非线性结构与线性结构的式子进行巧妙合理的转换,从而达到避繁就简,化难为易之目的。本文略举数例,以抛砖引玉之鉴。一、非线性结构转换为线性结构例1 若x、y、z均为小于1的正实数,试证x(1-y)+y(1-z)+z(1-x)<1。分析:这个待证关系式呈非线性结构形式,现在我们把其中的y、z看成常量,而把x看成变量,就转换成关于x的线性结构形式,也就是关于x的一次不等式,因此可借助于一次函数的图象特征予以解决。
Using dialectical viewpoints, some non-linear structural and linear structural equations in mathematics problems can be subtly and reasonably converted, so as to avoid complications, make conciseness, and eliminate difficulties. This article gives a few examples to give you an introduction. First, the nonlinear structure is converted to a linear structure Example 1 If x, y, z are positive real numbers less than 1, test x (1-y) + y (1-z) + z (1-x) <1. Analysis: This relationship is a non-linear structure, and now we consider the y and z as constants, and considering x as a variable, we convert it into a linear structure about x, that is, an inequality about x. Therefore, it can be solved by means of the image feature of a linear function.