KuLuLu_MaTaTa
幼苗
共回答了424个问题 举报
因为m,n是方程X²-3X+1=0的两根,所以有n^2-3n+1=0,而且由韦达定理知m+n=3,m*n=1
代数式2m²+4n²-6n+1996=2m^2+2n^2+2(n^2-3n+1)+1994=2(m+n)^2-4m*n+2(n^2-3n+1)+1994
将n^2-3n+1=0,m+n=3,m*n=1代入上式得
2m²+4n²-6n+1996=2(m+n)^2-4m*n+2(n^2-3n+1)+1994=18-4+0+1994=2008
1年前
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