2016年5月7日福州高三质检文科数学含答案
本小题考查绝对值不等式的解法与性质、不等式的证明等基础知识，考查运算求解能力、推理论证能力，考查分类与整合思想、化归与转化思想等．满分10分． 解：（Ⅰ）由|x 3| 2x 1得， x 3, x 3,
或 ·································································· 2分
(x 3) 2x 1,x 3 2x 1, 解得x 2． 依题意m 2． ·························································································· 5分
11 11
（Ⅱ）因为x t x x t x t t ，
tt tt
1
当且仅当 x t x 0时取等号， ···························································· 7分
t
1
因为关于x的方程|x t| |x | 2（t 0）有实数根，
t
1
所以t 2． ························································································ 8分
t
另一方面，t 所以t
1
…2， t
1
2， ························································································ 9分 t
所以t 1或t 1． ·················································································· 10分
