一道清华数学题的推导过程

m+n+p=0
m^2+n^2+p^2=4
m^4+n^4+p^4=?

解：
m+n=-p
(m+n)^2=p^2
(m^2+n^2)+2mn=p^2
(4-p^2)+2mn=p^2
2mn=2p^2-4
mn=p^2-2

(m^2+n^2)^2=(4-p^2)^2
m^4+2m^2n^2+n^4=(4-p^2)^2
m^4+2(p^2-2)^2+n^4=(4-p^2)^2
m^4+2(4-4p^2+p^4)+n^4=16-8p^2+p^4
m^4+n^4+p^4=8