已知m^2=2n+5,n^2=2m+5,且m不等于n,求m^3-4mn+n^3的值

m^3-4mn+n^3=m(2n+5)-4mn+n(2m+5)
=5m+5n
m^2=2n+5,n^2=2m+5两个相减得
m^2-n^2=2(m-n)
因为m不等于n
m+n=2
所以上边得是10

m^2=2n+5,可变成 m^2-2n=5
同理，n^2=2m+5也可变成 n^2-2m=5
m^3-4mn+n^3
=m^3-2mn+n^3-2mn
=m( m^2-2n)+n(n^2-2m)
再将最上面演变后的公式代进去
那么原式=5m+5n
=5(m+n)