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配方法的思想对我们初中生来说是一种崭新的思维方式。当某些数学问题的研究讨论陷入僵持时,配方法常常能给予巧妙的配合,使我们突然间获得解决问题的方法和结果。 [例1] 化简(5+12(3+2(2~(1/2)))~(1/2))~(1/2) 解:原式=(5+12((2~(1/2)+1)~2)~(1/2))~(1/2) =(17+12(2~(1/2)))~(1/2) =(3~2+12(2~(1/2))+((2(2~(1/2)))~2))~(1/2) =((3+2(2~(1/2)))~2)~(1/2) =3+2(2(1/2)) [例2] 已知:x~2+y~2+z~2+1/x~2+1/y~2+1/z~2=6,求证:xyz(x+y+z)=xy+yz+zx
The idea of matching methods is a new way of thinking for junior high school students. When the study and discussion of certain mathematical problems is deadlocked, the matching method can often give clever cooperation so that we suddenly get the solution to the problem and the results. [Example 1] Simplification (5+12(3+2(2~(1/2)))~(1/2))~(1/2) Solution: Original formula=(5+12((2~ (1/2)+1)~2)~(1/2))~(1/2) =(17+12(2~(1/2)))~(1/2)=(3~2 +12(2~(1/2))+((2(2~(1/2)))~2))~(1/2) =((3+2(2~(1/2)) )~2)~(1/2) =3+2(2(1/2)) [Example 2] Known: x~2+y~2+z~2+1/x~2+1/y ~2+1/z~2=6, verification: xyz(x+y+z)=xy+yz+zx