求(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)的值.其中有四个选项,分别是:A.2^65+1 B.2^65 C.2^128-1 D.2^128
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![求(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)的值.其中有四个选项,分别是:A.2^65+1 B.2^65 C.2^128-1 D.2^128](/uploads/image/z/1732884-60-4.jpg?t=%E6%B1%82%282%2B1%29%282%5E2%2B1%29%282%5E4%2B1%29%282%5E8%2B1%29%282%5E16%2B1%29%282%5E32%2B1%29%282%5E64%2B1%29%E7%9A%84%E5%80%BC.%E5%85%B6%E4%B8%AD%E6%9C%89%E5%9B%9B%E4%B8%AA%E9%80%89%E9%A1%B9%2C%E5%88%86%E5%88%AB%E6%98%AF%EF%BC%9AA.2%5E65%2B1+B.2%5E65+C.2%5E128-1+D.2%5E128)
求(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)的值.其中有四个选项,分别是:A.2^65+1 B.2^65 C.2^128-1 D.2^128
求(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)的值.
其中有四个选项,分别是:
A.2^65+1 B.2^65 C.2^128-1 D.2^128
求(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)的值.其中有四个选项,分别是:A.2^65+1 B.2^65 C.2^128-1 D.2^128
(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
原式=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=(2^16-1)(2^16+1)(2^32+1)(2^64+1)
=(2^32-1)(2^32+1)(2^64+1)
=(2^64-1)(2^64+1)
=2^128-1
用平方差公式