试题分析:(1)先因式分解把原不等式转化为.再对三个根的大小进行讨论求解. (2)解本小题的关键是把,, ∴恒成立,最终转化为恒成立来解决,然后再构造函数求最值即可. (1) ·························· 1分 ①················· 3分 ② p = 2时,解集为····················· 5分 ③ p > 2时,解集为·················· 7分 (2) ··························· 8分 ∴恒成立 ∴恒成立················· 9分 ∵上递减···················· 10分 ∴····························· 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. |