搜搜做题作业网计算:(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)
来源：学生作业帮 编辑：搜搜做题作业网作业帮 分类：数学作业 时间：2024/06/15 05:49:16
计算:(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)
(1)当x不等于1
(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)
=[(x-1)(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)]/(x-1)
=[(x^2-1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)]/(x-1)
=[(x^4-1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)]/(x-1)
=(x^32-1)(x^32+1)/(x-1)
=(x^64-1)/(x-1)
(2)当x等于1
结果是2^6=64
(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)
=[(x-1)(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)]/(x-1)
=[(x^2-1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)]/(x-1)
=[(x^4-1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)]/(x-1)
=(x^32-1)(x^32+1)/(x-1)
=(x^64-1)/(x-1)
(2)当x等于1
结果是2^6=64
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