Re: [其他] 求值的範圍.....
※ 引述《harry921129 (哈利~~)》之銘言：
: 大家好 先在這邊預祝各位年快樂
: 在這邊有一個東西想向各位請教
: 若 1/2 < x < 1
: 0< y < 1/2
: 且 3xy-2x-y+1=0
: 試求 x-xy 值的範圍
: 這個有辦法求得出來嗎
3(x - 1/3)(y - 2/3) = -1/3
(1)y = - x + 1
3x(-x + 1) - 2x - (-x + 1) + 1 = 0
=> 3x^2 - 2x = 0
=> x = 0, 2/3
(2)y = 0
-2x + 1 = 0
=> x = 1/2
(3)y = 1/2
(3/2)x - 2x + 1/2 = 0
=> x = 1
F(x, y) = x - xy = (1/3)(x - y + 1)
當x = 2/3, y = 1/3 => F_min = (1/3)(4/3) = 4/9
當x = 1/2, y = 0 => F = (1/3)(3/2) = 1/2
當x = 1, y = 1/2 => F = (1/3)(3/2) = 1/2
=> 4/9 < x - xy < 1/2
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