設(shè)m(x,y)
直線ob過(guò)原點(diǎn),則直線ob解析式為正比例函數(shù)
則設(shè)直線ob:y=kx
又b=(0,0)+(5,1)=(5,1)
則將b(5,1)代入y=kx
得k=1/5,則y=1/5*x
又m在直線上ob上
則m(x,y)也滿足y=1/5*x
又ma=(1,7)-(x,y)=(1-x,7-y)
mb=(5,1)-(x,y)=(5-x,1-y)
則ma*mb=(1-x,7-y)*(5-x,1-y)
=(1-x)*(5-x)+(7-y)*(1-y)
又y=1/5*x
則ma*mb=(1-x)*(5-x)+(7-y)*(1-y)
=x^2-6x+5+(7- x/5)*(1- x/5)
=x^2-6x+5+ x^2/25- 8x/5 +7
=26x^2/25 -38x/5 +12
則當(dāng)x=-(-38/5)/[2*(26/25)]=85/26
ma*mb最小=1026/13