m,n满足等式m^2=5n-2,n^2=5m-2,m不等于n,试求m+n的值 m^3-5mn-2n的值

题目

m,n满足等式m^2=5n-2,n^2=5m-2,m不等于n,试求m+n的值 m^3-5mn-2n的值
我脑袋转不过来!

答案

m^2=5n-2,
n^2=5m-2,
两式相减,得
m²-n²=5(n-m)
(m+n)(m-n)=5(n-m)
m+n=-5
m^2=5n-2,
m^2-5n=-2
m^3-5mn-2n
=m(m^2-5n)-2n
=m*(-2)-2n
=-2(m+n)
=-2*-5
=10