由(a+b)(a-b)引发的数学题计算:(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/02 17:07:17
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由(a+b)(a-b)引发的数学题计算:(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
由(a+b)(a-b)引发的数学题
计算:(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
由(a+b)(a-b)引发的数学题计算:(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)÷2
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)÷2
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)÷2
=(3^8-1)(3^8+1)(3^16+1)(3^32+1)÷2
=(3^16-1)(3^16+1)(3^32+1)÷2
=(3^32-1)(3^32+1)÷2
=(3^64-1)÷2
=1716841910146256242328924544640
(3-1)/2(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
=1/2 (3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
=1/2(3^4-1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
=1/2(3^8-1)(3^8+1)(3^16+1)(3^32+1)
=1/2(3^16-1)(3^16+1)(3^32+1)
=1/2(3^32-1)(3^32+1)
=1/2(3^64-1)
原式=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1) /(3-1)=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)/(3-1)=……=(3^64-1)/(3-1)=……