恩格尔系数对于美国:证明m(m+1)(m+2)(m+3)+1是一个完全平方式

来源:百度文库 编辑:高校问答 时间:2024/03/29 10:14:54

m(m+1)(m+2)(m+3)+1
=m(m+3)(m+1)(m+2)+1
=(m^2+3m)(m^2+3m+2)+1
=(m^2+3m)[(m^2+3m)+2]+1
=(m^2+3m)^2+2(m^2+3m)+1
=[(m^2+3m)+1]^2

标准答案!!!!!
证明: 原式=m(m+1)(m+2)(m+3)+1
=m(m+3)(m+1)(m+2)+1
=(m^2+3m)(m^2+3m+2)+1
=(m^2+3m)[(m^2+3m)+2]+1
=(m^2+3m)^2+2(m^2+3m)+1
=[(m^2+3m)+1]^2
所以m(m+1)(m+2)(m+3)+1是一个完全平方式

m(m+1)(m+2)(m+3)+1
=m(m+3)(m+1)(m+2)+1
=(m^2+3m)(m^2+3m+2)+1
=(m^2+3m)[(m^2+3m)+2]+1
=(m^2+3m)^2+2(m^2+3m)+1
=[(m^2+3m)+1]^2

很简单啊