設(2x²＋2kx＋k)/(4x²＋6x＋3)＜1,對一切實數x均成立,則實數k之範圍為多少?
2007-02-23 16:36:19 · 1 個解答 · 發問者 阿銘 1 in 教育與參考 ➔ 考試
各位要算得很精確ㄛ^_^!!!
2007-02-23 16:37:59 · update #1
4x²ï¼6xï¼3 => 4 > 0, 6*6 - 4*4*3 < 0
=> æ以 4x²ï¼6xï¼3 > 0
(2x²ï¼2kxï¼k)/(4x²ï¼6xï¼3)ï¼1
=> 2x²ï¼2kxï¼k < 4x²ï¼6xï¼3
=> 2x²ï¼(6-2k)xï¼(3-k) > 0
å çº å°ä¸åå¯¦æ¸ x åæç«
=> (6-2k)² - 4*2*(3-k) < 0
=> 4k² - 16kï¼ 12 < 0
=> k² - 4kï¼ 3 < 0
=> (k - 1)(k - 3) < 0
=> 1 < k < 3
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2007-02-24 00:38:11 · answer #1 · answered by JJ 7 · 0⤊ 0⤋