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问题 解答题

已知集合A={x|log2（x-1）＜1}，集合B={x|x2-ax+b＜0，a，b∈R}．

（1）若A=B，求a，b的值；

（2）若b=3，且A∪B=A，求a的取值范围．

答案

（1）由log2（x-1）＜1得0＜x-1＜2，所以集合A={x|1＜x＜3}．                  （2'）

由A=B知，x2-ax+b＜0的解集为{x|1＜x＜3}，所以方程x2-ax+b=0的两根分别为1和3．

由韦达定理可知，

a=1+3
b=1×3
，解得a=4，b=3，即为所求．                      （4'）

（2）由A∪B=A知，B⊆A．                                           （5'）

①当B=∅时，有△=a2-12≤0，解得-2

3
≤a≤2
3
；                         （7'）

②当B≠∅时，设函数f（x）=x2-ax+3，其图象的对称轴为x=

a
2
，则
△=a2-12＞0
f(1)=4-a≥0
f(3)=12-3a≥0
1＜
a
2
＜3

解得2

3
＜a≤4．                             （11'）

综上①②可知，实数a的取值范围是[-2

3
，4]．                            （12'）

单项选择题

黄疽最具特征的表现是

A．面黄

B．目黄

C．小便黄

D．恶心、纳呆

E．腹胀、呕吐
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填空题

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This debate is a crucial one in many cultures throughout the world (8) . In the US, the debate promises to impact the way we educate our children—that is, (9) manner and shape in which culture reproduces itself—and the way we write our laws. In (10) countries, equally crucial issues are at stake.
For many people, what is at stake is the character (11) US national identity. Hirsch argues that this identity needs to become less culturally fragmented; others, like Walker, (12) that the national character gets its strength from cultural diversity, from the freedom (at home and in (13) ) to celebrate, honor, and reproduce different cultural traditions. Those who take this latter view follow the reasoning (14) Shweder, arguing that we need to accept that there are multiple valid cultural perspectives and that two (15) perspectives can both be valid even though they might contradict one another.
Recognize that the position you (16) in this debate about culture—whatever position you take—is a political one with implications (17) what we should value, what we should praise, what we should accept, what we should teach. When (18) reflect on this debate, when you contribute your own voice to the discussion, try to be (19) of the implications that follow from your position. When you listen to the voices of others, try to (20) with awareness, deciding for yourself what is at stake and how their positions relate to your own.
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