→ Honor1984 : (3c - 4)^2 - 4(9c^2 - 12c + 5) 更改為 >= 0以下同 08/20 00:45
推 liang6159 : 感謝H大 08/20 08:58
※ 引述《liang6159 (liang6159)》之銘言：
: 設a,b,c為實數，已知a+2b+3c=4且2ab+6bc+3ac=5，若c最大值M，c最小值m，則M+m=?答案是8/9請教如何解題，謝謝!
a + 2b = 4 - 3c
2ab + 3c(2b + a) = 5
=> 2ab + 3c(4 - 3c) = 5
=> 2ab = 5 - 12c + 9c^2
(5 - 12c + 9c^2)/(a) + a = 4 - 3c
=> a^2 + (3c - 4)a + (9c^2 - 12c + 5) = 0
=> (3c - 4)^2 - 4(9c^2 - 12c + 5) > 0
=> 27c^2 - 24c + 4 < 0
=> M + m = 24/27 = 8/9
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