Question

m.n是整数求证A=1/2[m^4+n^4+(m+n)^4]是完全平方式

Answer 1

A=1/2[m^4+n^4+(m+n)^4]

=1/2[(m^2+n^2)^2+(m^2+2mn+n^2)^2-2m^2n^2]

=1/2[2(m^2+n^2)^2+4mn(m^2+n^2)+2m^2n^2]

=(m^2+n^2)^2+2mn(m^2+n^2)+m^2n^2

=(m^2+mn+n^2)^2

是一个完全平方式