試題分析:(1)先因式分解把原不等式轉(zhuǎn)化為
.再對三個根的大小進行討論求解.
(2)解本小題的關鍵是把
,
,
∴
恒成立,最終轉(zhuǎn)化為
恒成立來解決,然后再構(gòu)造函數(shù)求最值即可.
(1)
·························· 1分
①
················· 3分
② p = 2時,解集為
····················· 5分
③ p > 2時,解集為
·················· 7分
(2)
··························· 8分
∴
恒成立
∴
恒成立················· 9分
∵
上遞減···················· 10分
∴
····························· 11分
∴ p > 2 12分
點評:(1)分式不等式求解時一般要用數(shù)軸穿根法求解.(2)不等式恒成立問題一般要注意參數(shù)與變量分離,然后轉(zhuǎn)化為函數(shù)最值來研究.