若N为正整数,且X≠Y,试计算(x-y)的三N此方 - 知识问答

若N为正整数,且X≠Y,试计算(x-y)的三N此方*(y-x)的二N此方/(y-x)的五N此方

1个回答

(x-y)^3n
=[(x-y)^3]^n
=[-(y-x)^3]^n
所以
n是奇数,原式=-(y-x)^3n*(y-x)^2n/(y-x)^5n
=-(y-x)^5n/(y-x)^5n
=-1
n是偶数,原式=(y-x)^3n*(y-x)^2n/(y-x)^5n
=(y-x)^5n/(y-x)^5n
=1

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