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

m^2=n+2,n^2=m+2

m^2+m^2=m+n+4

m^2-n^2=(m+n)(m-n)=n-m

=>m+n=-1

m^2+n^2=m+n+4=3

mn=1/2*[(m+n)^2-(m^2+n^2)]=-1

代入

m^3-2mn+n^3

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

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

=(m+n)(m+n+4-mn)-2mn

=-1*(3+1)+2

=-4+4

=-2