Question

已知m^2=n+2,n^2=m+2,且m≠0,求m^3-2mn+n^3的值.

Answer 1

是否是m≠0为m≠n

由m^2=n+2,n^2=m+2两式相减得,m^2-n^2=n-m即(m-n)(m+n+1)=0,又m≠n,所以m-n≠0,所以,m+n+1=0,解得m+n=-1,因此m^3-2mn+n^3=m^3-mn+n^3-mn=m(m^2-n)+n(n^2-m)=2m+2n=2(m+n)=2×（-1）=-2