已知m,n是方程x-3x+1=0的两个根,求代数式2m+4n-6n+1996的值.
问题描述:
已知m,n是方程x-3x+1=0的两个根,求代数式2m+4n-6n+1996的值.
答
∵m,n是方程X-3X+1=0的两根,∴m+m=3,mn=1,2m+4n-6n+1996 =2m^2+2n^2+2n^2-6n+1996 =2(m^2+n^2)+2(n^2-3n)+1996 =2[(m+n)^2-2mn]+2*(-1)+1996 =2(3^2-2)-2+1996 =2*7+1994 =14+1994 =2018