要使三点A(1,2),B(3,1),C(2,3)到直线x-my=0的距离平方和取最大值,实数m的值应是多少?

问题描述:

要使三点A(1,2),B(3,1),C(2,3)到直线x-my=0的距离平方和取最大值,实数m的值应是多少?

f(m)=|1-m*2|^2/(1+m^2)+|3-m*1|^2/(1+m^2)+|2-3m|^2/(1+m^2)=(1-4m+4m^2+9-6m+m^2+4-12m+9m^2)/(1+m^2)=(14m^2-22m+14)/(1+m^2)=14-22m/(m^2+1)=14-22/(m+1/m)1、当m=0时,f(m)=142、当m14-22/(m+1/m)≥14-22/...