关于数学的两道难题,高手请进~~!⑴(2+1)(2∧2+1)(2∧4+1)… … (2∧32+1)+1⑵已知A+B=5,AB=-4.求A∧+B∧请各位大虾写出解题步骤,好的话追加20分,谢谢拉~~!
2019-04-13
关于数学的两道难题,高手请进~~!
⑴(2+1)(2∧2+1)(2∧4+1)… … (2∧32+1)+1
⑵已知A+B=5,AB=-4.求A∧+B∧
请各位大虾写出解题步骤,好的话追加20分,谢谢拉~~!
优质解答
⑴(2+1)(2^2+1)(2^4+1)……(2^32+1)+1
原式
=(2-1)(2+1)(2^2+1)(2^4+1)……(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)……(2^32+1)+1
=(2^4-1)(2^4+1)……(2^32+1)+1
=(2^8-1)……(2^32+1)+1
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64
通过乘以(2-1)这一项,不断的构成平方差；
⑵已知A+B=5,AB=-4,求A²+B².
A²+B²
=(A+B)²-2AB
=5²-2×(-4)
=25+8
=33
⑴(2+1)(2^2+1)(2^4+1)……(2^32+1)+1
原式
=(2-1)(2+1)(2^2+1)(2^4+1)……(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)……(2^32+1)+1
=(2^4-1)(2^4+1)……(2^32+1)+1
=(2^8-1)……(2^32+1)+1
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64
通过乘以(2-1)这一项,不断的构成平方差；
⑵已知A+B=5,AB=-4,求A²+B².
A²+B²
=(A+B)²-2AB
=5²-2×(-4)
=25+8
=33