數學 絕對直不等式詳解

因為 0小於 l2x+1l < l x-3l

所以, 可以將不等式的兩邊平方

l2x+1l ^2< l x-3l^2

4x^2+4x+1< x^2-6x+9

3x^2+10x - 8<0

(x+4)(3x-2) <0

得到解為 -4 < x < (2/3)

Blog: http://tw.myblog.yahoo.com/math-life

The answer is as follows:

| 2x + 1 | < | x - 3 |

| 2x + 1 |^2 < | x - 3 |^2

4x^2 + 4x + 1 < x^2 - 6x + 9

3x^2 + 10x - 8 = 0

(x + 4)(3x - 2) = 0

Ans: -4 < x < 2/3 ...... (ans)

2011-05-29 04:39:58 補充：
In the last second line and last third line, the "=" should be "<', i.e.

3x^2 + 10x - 8 < 0

(x + 4)(3x - 2) < 0

怪了, 一直沒辦法回答, 你自己去參考以下網址吧!

http://tw.myblog.yahoo.com/jw!JCVbjQyaBRbXTWOakincl1.Wpxbobg--/article?mid=9209