(3+1)(3²+1)(3四次方+1)(3八次方+1)(3十六次方+1)
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 08:36:26
![(3+1)(3²+1)(3四次方+1)(3八次方+1)(3十六次方+1)](/uploads/image/z/575730-18-0.jpg?t=%EF%BC%883%2B1%EF%BC%89%EF%BC%883%26%23178%3B%2B1%EF%BC%89%EF%BC%883%E5%9B%9B%E6%AC%A1%E6%96%B9%2B1%EF%BC%89%EF%BC%883%E5%85%AB%E6%AC%A1%E6%96%B9%2B1%EF%BC%89%EF%BC%883%E5%8D%81%E5%85%AD%E6%AC%A1%E6%96%B9%2B1%EF%BC%89)
(3+1)(3²+1)(3四次方+1)(3八次方+1)(3十六次方+1)
(3+1)(3²+1)(3四次方+1)(3八次方+1)(3十六次方+1)
(3+1)(3²+1)(3四次方+1)(3八次方+1)(3十六次方+1)
用平方差
原式=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/(3-1)
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/2
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)/2
=(3^8-1)(3^8+1)(3^16+1)/2
=(3^16-1)(3^16+1)/2
=(3^32-1)/2
原式=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/(3-1)
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/(3-1)
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)/(3-1)
=(3^8-1)(3^8+1)(3^16+1)/(3-1)
=(3^16-1)(3^16+1)/2
=(3^32-1)/2