题目

(a+1/a)(a^2+1/a^2)(a^4+1/a^4)(a^8+1/a^8)(a^16+1/a^16)(a^32+1/a^32)(a^2-1)

提问时间：2021-03-27

答案

原式 = [原式 *（a-1/a）]/（a-1/a） 注：方差公式
=[(a^2-1/a^2)(a^2+1/a^2)(a^4+1/a^4)(a^8+1/a^8)(a^16+1/a^16)(a^32+1/a^32)(a^2-1)]/(a-1/a)
=[(a^4-1/a^4)(a^4+1/a^4)(a^8+1/a^8)(a^16+1/a^16)(a^32+1/a^32)(a^2-1)]/(a-1/a)
=[(a^8-1/a^8)(a^8+1/a^8)(a^16+1/a^16)(a^32+1/a^32)(a^2-1)]/(a-1/a)
=[(a^16-1/a^16)(a^16+1/a^16)(a^32+1/a^32)(a^2-1)]/(a-1/a)
=[(a^32-1/a^32)(a^32+1/a^32)(a^2-1)]/(a-1/a)
=[(a^64-1/a^64)(a^2-1)]/(a-1/a)
分子分母同时乘以a/[a^2-1]
原式=(a^64-1/a^64)*a
=a^65-1/a^63