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配方法是初中数学中最基本而又最重要的数学方法。通过配方法配出的是两个(或几个)数的和或差的平方,是完全平方式,而完全平方式表示非负数,我们可以利用这些性质来解决某些竞赛题。一、通过配方法配出的是两个(或几个)数的和或差的平方,是完全平方式,我们可以把这个完全平方式看作一个整体,而不必分别考虑所求问题中每个字母的值。例1:已知 a=1999x+2000,b=1999x+2001,c=1999x+2002,则多项式 a~2+b~2+c~2-ab-bc-ca①的值是。(2002年全国初中数学联赛题)(A)0 (B)2 (C)2 (D)3解:①式=1/2[(a-b)~2+(b-c)~2+(c-a)~2]=1/2[(-1)~2+(-1)~2+2~2]:3。二、配出完全平方式,化简根式。
The matching method is the most basic and important mathematical method in junior high school mathematics. The matching method is used to match the sum or difference squares of two (or several) numbers. It is a completely flat pattern, and the completely flat pattern represents a non-negative number. We can use these properties to solve certain competition problems. First, the matching method is used to match the sum or difference squares of two (or several) numbers. It is a completely flat method. We can treat this completely flat pattern as a whole without having to consider each question separately. Letter values. Example 1: Given that a=1999x+2000, b=1999x+2001, and c=1999x+2002, the values of the polynomials a~2+b~2+c~2-ab-bc-ca1 are. (2002 national junior high school mathematics league title) (A) 0 (B) 2 (C) 2 (D) 3 solutions: 1 formula = 1/2 [(ab) ~ 2+ (bc) ~ 2+ (ca) ~ 2]=1/2[(-1)~2+(-1)~2+2~2]:3. Second, match out completely flat and simplify rooting.