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:作业帮 分类:数学作业 时间:2024/05/06 11:49:23
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
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