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

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

m，n 是方程x²=5x-2 的2个根

x²-5x+2=0
m+n=5

mn=2

m³-5mn-2n
=m×m²-5mn-2n
=m×（5n-2）-5mn-2n
=-2m-2n
=-10