已知m^2=n+2,n^2=m+2(m≠0) 求m^3-2mn+n^3=?
问题描述:
已知m^2=n+2,n^2=m+2(m≠0) 求m^3-2mn+n^3=?
答
m^2=n+2,n^2=m+2(m≠0)
m^2-n^2=n+2-m-2
(m+n)(m-n)=-(m-n)
m+n=-1
m^3-2mn+n^3
=m(n+2)-2mn+n(m+2)
=mn+2m-2mn+mn+2n
=2m+2n
=2(m+n)
=2*(-1)
=-2