试题分析:(1)先因式分解把原不等式转化为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232353566541008.png)
.再对三个根的大小进行讨论求解.
(2)解本小题的关键是把
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823235356732895.png)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823235356748832.png)
,
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823235356764982.png)
恒成立,最终转化为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232353567791184.png)
恒成立来解决,然后再构造函数求最值即可.
(1)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232353566541008.png)
·························· 1分
①
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232353565761456.png)
················· 3分
② p = 2时,解集为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823235356608684.png)
····················· 5分
③ p > 2时,解集为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823235356639942.png)
·················· 7分
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823235356732895.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823235356748832.png)
··························· 8分
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823235356764982.png)
恒成立
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232353569511190.png)
恒成立················· 9分
∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823235356966983.png)
上递减···················· 10分
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823235356982744.png)
····························· 11分
∴ p > 2 12分
点评:(1)分式不等式求解时一般要用数轴穿根法求解.(2)不等式恒成立问题一般要注意参数与变量分离,然后转化为函数最值来研究.