已知点M（6,5,1）,N（3,2,2）,点P在xOy平面上,则｜PM｜+｜PN｜的最小值为

P(x,y,0)
｜PM｜+｜PN｜
=√[(x-6)^2+(y-5)^2+(0-1)^2]+√[(x-3)^2+(y-2)^2+(0-2)^2]
≥2{[(x-6)^2+(y-5)^2+(0-1)^2]*[(x-3)^2+(y-2)^2+(0-2)^2]}^(1/4)
等号当且仅当(x-6)^2+(y-5)^2+(0-1)^2=(x-3)^2+(y-2)^2+(0-2)^2成立,
(x-6)^2+(y-5)^2+(0-1)^2=(x-3)^2+(y-2)^2+(0-2)^2,有x+y-15/2=0
(x-6)^2+(y-5)^2+(0-1)^2
=(3/2-y)^2+(y-5)^2+(0-1)^2
=2y^2-13y+113/4
=2(y-13/4)^2+57/8
≥57/8,等号当且仅当x=17/4,y=13/4成立
｜PM｜+｜PN｜的最小值为
2{[(x-6)^2+(y-5)^2+(0-1)^2]*[(x-3)^2+(y-2)^2+(0-2)^2]}^(1/4)
=2[(x-6)^2+(y-5)^2+(0-1)^2]^(1/2)
=2*(57/8)^(1/2)
=√114/2