Question

已知m,n是方程x^2-2x-1=0的两根,且(7m^2-14m-3)(3n^2-6n+500)的值

Answer 1

m,n是方程x^2-2x-1=0的两根

∴m²-2m=1,n²-2n=1

∴(7m^2-14m-3)(3n^2-6n+500)

=[7(m²-2m)-3][3(n²-2n)+500]

=[7*1-3][3*1+500]

=4*503

=2012