某抛物线y=2x^2上两点A(x1,y1),B(x2,y2)关于直线y=x+m对称,有x1x2=-1/2,则m=

y1=2x1^2y2=2x2^2对称,则有：中点在此直线上：(y1+y2)/2=(x1+x2)/2+m,斜率为-1：y1-y2=-(x1-x2)所以：2(x1^2-x2^2)=-(x1-x2)--->x1+x2=-1/2m=(y1+y2-x1-x2)/2=x1^2+x2^2-(x1+x2)/2=(x1+x2)^2+2x1x2+1/4=1/4+1+1/4=3/...