→ coffee40702 : 3log2<2log3吧 04/09 23:41
※ 編輯: Honor1984 (220.141.68.84), 04/10/2015 01:33:40
※ 引述《coffee40702 (阿維)》之銘言：
: y=ax^2 + bx + c 通過(1, log2)、(2, log3)、(3, log4)三點下列何者正確？
: (1)a>0
: (2)b>0
: (3)c>0
: (4)b^2 - 4ac >0
: (5) |a| >|c|
: 把點帶進去算算出a,b,c的值好像很慢，考試應該會寫很久，有比較快的算法嗎？
log2 + log4 = 3log2 < 2log3
=> a < 0 (1)錯
-b/2a > 2
=> b > 4|a| > 0 (2)對
b^2 - 4ac > 0 (4)對
a = (1/2)[log(4/3) - log(3/2)]
= (1/2)log(8/9) = -(1/4)log(3 / 2√2) > -(1/4)log(3/2)
=> |a|/log(3/2) < 1/4
0 > a > log(2/3)
(5/2)log(8/9) + b = log(4/3)
c = log2 + 2log(8/9) - log(4/3)
= log(3/2) + 2log(8/9) > 0 (3)對
= log(3/2) - 4|a|
|c|/|a| = 2[log(3/2)/|a|] - 4 > 1
=> |c| > |a|
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