已知m+n+p=0,那么:
m+p=-n,n+m=-p,p+n=-m
所以:
(m^2+n^2-p^2)分之一+(n^2+p^2-m^2)分之一+(p^2+m^2-n^2)分之一
=[n²+(m+p)(m-p)]分之1+[p²+(n+m)(n-m)]分之1+[m²+(p+n)(p-n)]分之1
=[n²-n(m-p)]分之1+[p²-p(n-m)]分之1+[m²-m(p-n)]分之1
=[n(n-m+p)]分之1+[p(p-n+m)]分之1+[m(m-p+n)]分之1
=[n(-m-m)]分之1+[p(-n-n)]分之1+[m(-p-p)]分之1
=(-2mn)分之1+(-2pn)分之1+(-2mp)分之1
=(-2mnp)分之(p+m+n)
=0