推 i0938652728 : 我想用算幾不等式去找 02/05 14:10
※ 引述《inch01742 (穎奇種筍子)》之銘言：
: 想請教第20題，答案是2，4，3
: http://i.imgur.com/hObmfGH.jpg
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: Sent from JPTT on my Samsung SM-N9208.
x = log_2 a
y = log_2 b
z = log_2 c
三數均正
抱歉符號重覆，以上x, y, z均非題目中的x, y, z
xy = x + y
=> 1 = 1/x + 1/y >= 2√[1/(xy)]
=> 0 < 1/(xy) <= 1/4
xyz = x + y + z
=> z = xy(z - 1)
=> 0 < 1 - (1/z) = 1/(xy) <= 1/4
=> 1 > 1/z >= 3/4
=> 1 < z <= 4/3
z = log_2 c <= 4/3
=> c <= 2^(4/3)
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