百度作业网计算(x+/1x)(x^2+1/x^2)(x^4+1/x^4)(x^8+1/x^8)(x^16+1/x^16)(x^2-
来源：学生作业帮 编辑：百度作业网作业帮 分类：数学作业 时间：2024/04/29 23:01:15
计算(x+/1x)(x^2+1/x^2)(x^4+1/x^4)(x^8+1/x^8)(x^16+1/x^16)(x^2-1)
(x+1/x)(x^2+1/x^2)(x^4+1/x^4)(x^8+1/x^8)(x^16+1/x^16)(x^2-1)
乘以(x-1/x)后同时再除以它
=(x-1/x)(x+1/x)(x^2+1/x^2)(x^4+1/x^4)(x^8+1/x^8)(x^16+1/x^16)(x^2-1)/(x-1/x)
=(x^2-1/x^2)(x^2+1/x^2)(x^4+1/x^4)(x^8+1/x^8)(x^16+1/x^16)(x^2-1)/(x-1/x)
＝……(多次运用平方差公式)
=(x^32-1/x^32)(x^2-1)/〔(x^2-1)/x〕
=(x^64-1)/x^32*x
=(x^64-1)/x^31
乘以(x-1/x)后同时再除以它
=(x-1/x)(x+1/x)(x^2+1/x^2)(x^4+1/x^4)(x^8+1/x^8)(x^16+1/x^16)(x^2-1)/(x-1/x)
=(x^2-1/x^2)(x^2+1/x^2)(x^4+1/x^4)(x^8+1/x^8)(x^16+1/x^16)(x^2-1)/(x-1/x)
＝……(多次运用平方差公式)
=(x^32-1/x^32)(x^2-1)/〔(x^2-1)/x〕
=(x^64-1)/x^32*x
=(x^64-1)/x^31
计算(x+/1x)(x^2+1/x^2)(x^4+1/x^4)(x^8+1/x^8)(x^16+1/x^16)(x^2-
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