数学解题过程就是不断地将未知转化成已知的过程,而构造法则是实现这种转化的重要手段之一。下面,笔者从例题分析谈起。例1正数x,y,x满足方程组{x~2+xy+y~2/3=25y~2/3+x~2=9x~2+xz+x~2=16试求:xy+2yx+3xz的值。分析:如果解方程组,求出x,y,z的值,再代人xy+2yz+3xz求值,显然很不容易,解题过程比较繁琐,令人望而生畏。其实,只要能注意到原方程组的 The process of mathematical problem solving is to continually transform the unknown into the known process, and the construction law is one of the important means to realize this transformation. Below, I talk about the analysis from the example. Example 1 Positive numbers x, y, x satisfy the system of equations {x ~ 2 + xy + y ~ 2/3 = 25y ~ 2/3 + x ~ 2 = 9x ~ 2 + xz + x ~ 2 = + 2yx + 3xz value. Analysis: If you solve the system of equations, find the value of x, y, z, and then replace xy +2 yz +3 xz evaluation, obviously not easy, solving the problem is more complicated, daunting. In fact, as long as we can notice the original equations