Question

已知m3次方=n+2 n3次方=m+2 求m3次方-2mn+n3次方

Answer 1

m^3=n+2,n^3=m+2
则m^3-n^3=n-m
m^3-n^3=(m-n)(m^2+mn+n^2)=n-m
(m^2+mn+n^2+1)(m-n)=0
1,m=n.则为0
2,m不等于n,则m^2+mn+n^2=-1,不好求了,是3次吗
如果是m的2次方=n+2 n的2次方=m+2
m^2=n+2,n^2=m+2
则m^2-n^2=n-m
(m+n)(m-n)=n-m
(m+n+1)(m-n)=0
m不等于n
所以m+n=-1
m^3-2mn+n^3
=mm^2-2mn+nn^2
=m(n+2)-2mn+n(m+2)
=mn+2m-2mn+mn+2n
=2(m+n)
=2*(-1)
=-2