一道关于巧算的数学题`
来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/06/25 02:25:18
一道关于巧算的数学题`
(1).(2+1)(2方+1)(2的4次方+1)(2的8次方+1)+1
(2).2006/(2006方-2005*2007)
那个*就是乘号,
(1).(2+1)(2方+1)(2的4次方+1)(2的8次方+1)+1
(2).2006/(2006方-2005*2007)
那个*就是乘号,
![一道关于巧算的数学题`](/uploads/image/z/610587-27-7.jpg?t=%E4%B8%80%E9%81%93%E5%85%B3%E4%BA%8E%E5%B7%A7%E7%AE%97%E7%9A%84%E6%95%B0%E5%AD%A6%E9%A2%98%60)
(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^4-1)(2^4+1)(2^8+1)+1
=(2^8-1)(2^8+1)+1
=2^16-1+1
=2^16
=65536
2006/(2006^2-2555*2007)
=2006/(2006^2-(2006-1)*(2006+1))
=2006/(2006^2-(2006^2-1))
=2006/1
=2006
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^4-1)(2^4+1)(2^8+1)+1
=(2^8-1)(2^8+1)+1
=2^16-1+1
=2^16
=65536
2006/(2006^2-2555*2007)
=2006/(2006^2-(2006-1)*(2006+1))
=2006/(2006^2-(2006^2-1))
=2006/1
=2006