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问题 解答题
设[x]表示不大于x的最大整数，集合A={x|x2-2[x]=3}，B={x|
1
8
＜2x＜8}，则A∩B=______．
答案

由集合B中的不等式得：2-3＜2x＜23，由2＞1，得到指数函数为增函数，

所以-3＜x＜3，则集合B=（-3，3），

由集合A中的等式x2-2[x]=3变形得：x2=2[x]+3，由题意可知x2为整数，

而x2-2x-3=0的解为x=-1或3，则[-1]=-1，[3]=3，

所以x2=2[x]+3=-2+3=1或x2=2×3+1=7，解得x=±1或x=±

7
，

经检验：x=1，x=-

7
不合题意舍去，所以x=-1或
7
，则集合A={-1，
7
}；

∴A∩B={-1，

7
}．

故答案为：{-1，

7
}．

阅读理解

阅读短文，根据短文内容回答问题。

     Sally's father is ill in hospital. and her mother has to look after her father there The woman can't

leave their four-year-old son Harry at home. So she asks Sally, "How many classes do you have this

afternoon?"

     "We have no classes today," answers the girl. "We're having a school sports meeting today."

     "That's great!" says her mother. "Take your brother to your school. Tell your teachers I have a lot

of things to do. I'm sure they can let you look after him today."

     Sally does what her mother says. This little boy comes to school for the first time and thinks

everything is interesting. He sees some children having a race and asks. "What are they running for,

Sally?"

     "The first one can get a prize." answers Sally.

     "Now, I see. But why are the others running?" 

1. Where is Sally's father?

    ____________________________________

2. Who will take care of Sally's father?

    ____________________________________

3. How old is Harry?

    ____________________________________

4. Does Harry often go to school?

    ____________________________________

5. Why does Sally take her brother to school today?

    ____________________________________
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判断题

对于一个自动调节系统，调整时间越长，意味着系统越稳定。（）
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