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

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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
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

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
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


因为m,n是方程x^2-2x-1=0的两根,
所以m²-2m-1=0 n²-2n-1=0
所以
7m^2-14m-3=7(m²-2m-1)+4=0+4=4
3n^2-6n+500=3(n²-2n-1)+503=0+503=503
所以
(7m^2-14m-3)(3n^2-6n+500)=4*503=2012