Question

已知：m*m=n+2,n*n=m+2.求m*m*m-2mn+n*n*n（m不等于n）。

Answer 1

解：
m^2=n+2 (1)
n^2=m+2 (2)
(1)-(2)
m^2-n^2=n-m
(m-n)(m+n)+(m-n)=0
(m-n)(m+n+1)=0
又m≠n，因此m+n+1=0 m=-(n+1)
代入n^2=m+2，整理，得
n^2+n-1=0

m^3-2mn+n^3
=-(n+1)^3+2(n+1)n+n^3
=-n^3-3n^2-3n-1+2n^2+2n+n^3
=-n^2-n-1
=-(n^2+n-1)-2
=-2

Answer 2

m2=m+2
m3=m(n+2)=mn+2m

n2=m+2
n3=n(m+2)=mn+2n

m2-n2=(n+2)-(m+2)
(m+n)(m-n)=-(m-n)
m≠n则m-n≠0
所以m+n=-1

原式=mn+2m-2mn+mn+2n
=2(m+n)
=2×(-1)
=-2