有趣的数学【17】：一切都有套路——解方程组法求解析式
解题和做人一样，存在着典型的问题。
一般碰到典型问题，就有对应的典型的解法去求解，这个就是套路。懂得了道路，问题就不再成为问题，而是简单的数字游戏了。
今天讲的这个套路，就是很常用的解方程组法求解析式。在数学解题过程中，若已知的函数关系较为抽象简约，则可以对变量进行置换，设法构造方程组，通过解方程组求得函数解析式。
先举例：
观察题面，发现用我们之前说的换元法，待定系数法在这里都用不上，那么就只能另辟蹊径了。
题目中，包含f(x)和f(-x)，所以，将x的位置用-x带入，则有
2f(-x) - f(x) = -x+1
这样就和原方程配成了一个方程组：
再观察这个方程组，可以看到相加可去除f(-x)，最后得到结果
f(x) = 1/3x+1
这就是解方程组法求解析式。
一般能够使用这个方法的题目有明显的特征，就是解析式里面含有：
f(x)和f(-x)，
f(x)和f(1/x)
这2种情况。
前者用-x代替x带入，后者用1/x代替x带入，得到一个新的方程，与原方程式组成一个方程组，然后想办法消除f(-x)或者f(1/x)项，就可以求出f(x)了。
这就是典型的套路，是一定要掌握的。
很多逃离北上广的人都说：
“城市套路深，我要回农村”可是不要忘了：
农村路也滑，人心更复杂。如果不能掌握套路，到了哪里都是被套的命。要改变的不是环境，而是自己。
附上解题草稿：
Posted from my blog with SteemPress : https://kissfirer.000webhostapp.com/maths17
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