回覆 1# aliher327 的帖子
第 15 題
令 c^2 + d^2 = 16
4OP + 5PA = 4√(a^2 + b^2) + 5√[(7 - a)^2 + (24 - b)^2 + 6^2]
= √(c^2 + d^2)√(a^2 + b^2) + √(c^2 + d^2 + 3^2)√[(7 - a)^2 + (24 - b)^2 + 6^2]
>= (ca + db) + [c(7 - a) + d(24 - b) + 18]
= 7c + 24d + 18
等號成立於 c/a = d/b 且 c/(7 - a) = d/(24 - b) = 3/6
即 24c = 7d，c = 28/25，d = 96/25
所求 = 7 * (28/25) + 24 * (96/25) + 18 = 118
