计算:(x+1/x)(x2+1/x2)(x4+1/x4)(x8+1/x8)(x2－1)

题目

计算:(x+1/x)(x2+1/x2)(x4+1/x4)(x8+1/x8)(x2－1)
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答案

(x+1/x)(x2+1/x2)(x4+1/x4)(x8+1/x8)(x2－1)=(x+1/x)(x2+1/x2)(x4+1/x4)(x8+1/x8)(x-1/x)(x)=(x2-1/x2)(x2+1/x2)(x4+1/x4)(x8+1/x8)(x)=(x4-1/x4)(x4+1/x4)(x8+1/x8)(x)=(x8-1/x8)(x)=x9-1/x7