Question

已知mn是方程x^2-2x-1=0的两根且7m平方减14m+a括号乘以3n平方减六n-7括号等于

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