MQ49 --- Inequality

圖片參考：http://i1096.photobucket.com/albums/g340/pingshek/2012-10-10.png?t=1349878243


http://i1096.photobucket.com/albums/g340/pingshek/2012-10-10.png?t=1349878243

2012-10-13 01:41:42 補充：
The answer should be changed to :
[-1 < 0 < 0 or x > 1] and [x ≤ (1-√5)/2 or 0 < x ≤ (1+√5)/2]

0 ≤ x ≤ (1+√5)/2 should be changed to 0 < x ≤ (1+√5)/2
This is because the fraction is meaningless when the denominator x² is 0.

2012-10-13 01:48:13 補充：
For f(x) = (x+1)x(x-1)/x² > 0
x² ≥ 0

When x > -1:
x+1 < 0, x < 0, x-1 < 0
Hence, f(x) < 0

When -1 < x < 0:
x+1 < 0, x < 0, x-1 > 0
Hence, f(x) > 0

When 0 < x < 1:
x+1 < 0, x > 0, x-1 > 0
Hence, f(x) < 0

When x > 1:
x+1 > 0, x > 0, x-1 > 0
Hence, f(x) > 0

Ans: -1 < x < 0 or x > 1

2012-10-13 01:49:59 補充：
Use similar method for [x-(1-√5)/2]x[x-(1+√5)/2]/x² ≤ 0

2012-10-15 23:26:50 補充：
There is a typo in the first 補充。

It should be :
"The last second step (NOT THE ANSWER) should be changed to
[-1 < 0 < 0 or x > 1] and [x ≤ (1-√5)/2 or 0 < x ≤ (1+√5)/2]"

2012-10-15 23:31:14 補充：
The answer should be unchanged. It should be :
-1 < x ≤ (1-√5)/2 or 1 < x ≤ (1+√5)/2

2012-10-15 23:32:01 補充：
What is meant by "If x &lt; 0, x - x⁻¹ will also < 0, which is not available!" ?

Actually, then answer should be - 1 ≤ x ≤ (1 - √5)/2 or 1 ≤ x ≤ (1 + √5)/2.