hh(310:17:59)方程x+1/x=1999的两根为m,n,则n2乘1-m3/(n-1)=?

Question

hh (31 0:17:59)
方程x+1/x=1999的两根为m,n,则n2乘1-m3/(n-1)=?

Answer 1

∵ x+1/x=1999∴ x²-1999x+1=0 ,∴ m+n=1999 ,mn=1 ,∴ n²(1-m^3)/(n-1)=n²(1-m)(1+m+m²)/(n-1)=n(1-m)×n(1+m+m²)/(n-1)=(n-mn)×(n+mn+m²n)/(n-1)=(n-1)×(n+1+m)/(n-1)=m+n+1=1999...