Question

已知：m^2=n+2，n^2=m+2，（m不等于n）。求m^3-2mn+n^3的值

Answer 1

因为m^2=n+2,n^2=m+2
所以 m^2-n^2=n-m
即 (m-n)(m+n)=-(m-n)
m+n=-1

m^3-2mn+n^3=m·m^2-2mn+n·n^2
=m(n+2)-2mn+n(m+2)
=mn+2m-2mn+mn+2n
=2(m+n)
因为m+n=-1 所以 原式=-2

Answer 2

2m+2n

追答

又因为m^2-n^2=n-n
所以m+n=-1
所以原式=-2