Question

已知 m的平方=n+2 (m不等于n) 求m的三次方-2mn+n的三次方

Answer 1

因为m^2=n+2,n^2=m+2

所以 m^2-n^2=（n+4）-(m+4)=n-m

即 (m-n)(m+n)=-(m-n)

m+n=-1

m^3-2mn+n^3=m·m^2-2mn+n·n^2

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

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

=4(m+n)

因为m+n=-1

所以m^3-2mn+n^3=-4