Inequalities
回答 (3)
2008-02-21 5:58 am
✔ 最佳答案
3/(x-2)>1[ 3/(x-2)](x-2)^2>(x-2)^2
3(x-2)>(x-2)^2
3x-6>x^2-4x+4
x^2-7x+10<0
(x-2)(x-5)<0
2<x<5
2008-02-21 8:10 am
3/(x - 2) > 1
3/(x - 2) * (x - 2)^2 > (x - 2)^2
3(x - 2) > (x - 2)^2
3(x - 2) - (x - 2)^2 > 0
(x - 2)(3 - x + 2) > 0
(x - 2)(-x + 5) > 0
(x - 2)(x - 5) < 0
2 < x < 5
開首跟第一位相同
但如第二位所說為免出錯
不 expend (x - 2)^2 為好
直接 fact
2008-02-21 00:11:35 補充：
亦無需分case
3/(x - 2) * (x - 2)^2 > (x - 2)^2
3(x - 2) > (x - 2)^2
3(x - 2) - (x - 2)^2 > 0
(x - 2)(3 - x + 2) > 0
(x - 2)(-x + 5) > 0
(x - 2)(x - 5) < 0
2 < x < 5
開首跟第一位相同
但如第二位所說為免出錯
不 expend (x - 2)^2 為好
直接 fact
2008-02-21 00:11:35 補充：
亦無需分case
2008-02-21 5:59 am
3/(x-2)>1
3/(x-2) - 1 >0
[3-(x-2)] / (x-2) > 0
(5-x)(x-2) > 0 as (x-2)^2 >=0
(x-5)(x-2)<0
2<5
2008-02-20 21:59:47 補充：
2
2008-02-20 22:02:36 補充：
typing mistake ~2< x < 5樓上做法同出一徹..不過多此一舉..因為最後要fact番倒不如一早通分母會比較快同減少運術錯誤既機會
3/(x-2) - 1 >0
[3-(x-2)] / (x-2) > 0
(5-x)(x-2) > 0 as (x-2)^2 >=0
(x-5)(x-2)<0
2<5
2008-02-20 21:59:47 補充：
2
2008-02-20 22:02:36 補充：
typing mistake ~2< x < 5樓上做法同出一徹..不過多此一舉..因為最後要fact番倒不如一早通分母會比較快同減少運術錯誤既機會
參考: myself
收錄日期: 2021-04-16 22:54:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080220000051KK03829