已知m^2+n^2=3,mn=-1,求多项式5m^2-3mn+12mn-7m^2+5n^2的值.
问题描述：
已知m^2+n^2=3,mn=-1,求多项式5m^2-3mn+12mn-7m^2+5n^2的值.
答
因为 m^2+n^2=3,mn=-1 所以(m+n)^2=1,(m-n)^2=5,n^2-m^2=(n+m)(n-m)=±√55m^2-3mn+12mn-7m^2+5n^2=-2m^2+9mn+5n^2＝(-2m^2+4mn-2n^2)+5mn+7n^2=-2(m+n)^2+7/2(m^2+2mn+n^2)+7/2(n^2-m^2)-2mn=7(1±√5)/2