Question

a=2001²+2001²x2002²+2002²证明完全平方

Answer 1

n=2001,n+1=2002

a=n^2+n^2*(n+1)^2+(n+1)^2

=n^2+n^2(n^2+2n+1)+(n^2+2n+1)

=n^2+n^4+2*n^3+n^2+n^2+2n+1

=n^4+2*n^3+3*n^2+2n+1

=n^2(n^2+n+1)+n(n^2+n+1)+(n^2+n+1) 这一步不太好明白,你可以试着倒回去算一下,是用拼凑的方法凑出来的.

=(n^2+2n+1)*(n^2+2n+1)

=(n^2+2n+1)^2完全平方数