[問題]高中問題
由 skywalker 於 星期六 九月 30, 2006 11:20 pm
#ed_op#DIV#ed_cl# 三角形ABC中,A(x1,y1) B(x2,y2) C(x3,y3) ,一點P使PA^2+PB^2+PC^2為最小,求P點座標#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#我是先令P(x,y)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# PA^2+PB^2+PC^2#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#=(x1-x)^2+(y1-y)^2+(x2-x)^2+(y2-x)^2+(x3-x)^2+(y3-y)^2#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#=x1^2+x2^2+x3^2+y1^2+y2^2+y3^2+3x^2+3y^2-2(x1*x)-2(x2*x)-2(x3*x)-2(y1*y)^2-2(y2*y)-2(y3*y)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#到這邊我救沒辦法配方把答案配出來,是我過程有錯嗎?還是一開始做法就錯了?#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#我知道座標是((x1+x2+x3)/3,(y1+y2+y3)/3),這個點是重心#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#