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“主元法”是一种特殊的解题方法,主要用于处理含有多个变量的数学问题.此法解题的关键在于将一个变量视为“主元”,其它变量均视为“常量”,使之化为我们熟悉的结构形式,从高层次上获取解题灵感.现例举此法在解题上的多种用途. (一)巧妙分解因式例1 分解因式m3-1-m2n-2mn+n2. 分析:若按部就班去分解,无“路”可走,但转换角度。视n为主元,则柳暗花明. 解:以n为主元,加以变形得原式=n2-(m2+2m)n+(m3-1) =[n-(m-1)][n-(m2+m+1)] =(n-m+1)(n-m2-m-1). (二)巧解方程
The “principal element method” is a special method of solving problems and is mainly used to deal with mathematical problems that contain multiple variables. The key to this method is to treat a variable as a “principal element” and other variables as “a constant. ” to make it a familiar structure form, and to obtain inspiration from a high level. Here are a few examples of how this method can be used to solve problems. (a) Cleverly factorize factor 1 and factorize m3-1 -m2n-2mn+n2. Analysis: If step by step decomposition, no ”Road" can go, but the conversion angle. If n is the main element, then the divinity is revealed. Solution: Take n as the principal element, and deform it to get the original formula=n2-(m2+2m)n+(m3-1) =[n-(m-1)][n-( M2+m+1)] =(n-m+1)(n-m2-m-1). (B) The solution equation