推 debdeb :謝謝XD 04/27 12:56
※ 引述《debdeb ()》之銘言：
: Find the range of values of the constant a for which there exist
: exactly two integers satisfying the two quadratic inequalities in x
: x^2 - 4x - 5 ≧ 0
: x^2 - (3a-2)x -6a ＜ 0
: simultaneously.
: 請問a的範圍該怎麼算？
: 謝謝！！
(x-(3a-2)/2)^2-6a-(3a-2)^2/4 < 0
(x-(3a-2)/2)^2 < (9a^2-12a+4+24a)/4 = (3a+2)^2/4
(i) a ≧ -2/3
-(3a+2)/2 < x-(3a-2)/2 < (3a+2)/2
-2 < x < 3a
but x ≧5 or x ≦ -1
hence, the integer solutions of x are -1, 5
then 5 < 3a < 6
(ii) a < -2/3
(3a+2)/2 < x-(3a-2)/2 < -(3a+2)/2
3a < x < -2
but x≧5 or x≦ -1
hence, the integer solutions of x are -3, -4
then -5 ≦ 3a < -4
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The range of a
5/3 < a < 2 or -5/3 ≦ a < -4/3
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