Question

已知m的平方=n+2,n的平方=m+2（m≠n）,求m³-2mn+n³

Answer 1

m^3-2mn+n^3

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

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

=2m-mn+mn+2n

=2(n+m)

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

相减：

(m+n)(m-n)=-(m-n)

m≠n

m+n=-1

原式=2*(-1)=-2