範例21

已知兩定點A(2, -1), B(4, 1)而P為直線x-y=0上之動點, 試求 之最小值.

[解法]

<Sol.>
設P=(t, t)
則 =<t-2, t+1>×<t-4, t-1>
=(t-2)(t-4)+(t+1)(t-1)
=(t²-6t+8)(t²-1)
=2t²-6t+7