长春恩德来假枝厂:已知3的16次方=43046721,求(3+1) (3的平方+1) (3的4次方+1) (3的8次方+1)

来源:百度文库 编辑:查人人中国名人网 时间:2024/05/08 19:30:54

两边同乘以二即(3-1)
(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)
=(3^4-1)(3^4+1)(3^8+1)
=(3^8-1)(3^8+1)
=3^16-1=43046720

所以原式=43046720/(3-1)=21523360
好好复习加油啊

(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)
=(3^4-1)(3^4+1)(3^8+1)
=(3^8-1)(3^8+1)
=3^16-1=43046720

因此原式=43046720/(3-1)=21523360

设原式为X,则
(3-1)X=3的16次方-1

2X=43046720

X=21523360