名校
1 . 已知集合
,其中
.对于
,
,定义
与
之间的距离为
.
(1)记
,写出所有
使得
;
(2)记
,
、
,并且
,求
的最大值;
(3)设
,
中所有不同元素间的距离的最小值为
,记满足条件的集合
的元素个数的最大值为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d9b434ed11c614630ad6a71bf1b196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53422543e9a9311416faf749bdda67b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1a7c3713945abc4eca8485945abf32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ebc8c7e32c1b561a908a36cfa2cbb5.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de36ac74e2640a897dedd876abcb63b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644d2ee36439bbc01fb4f35e9d24e5bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf15320a185c13d59087e9391485612.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d089503d05901e02113c0ed0bd59dff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a3b20462ba83086d0711a25ed83bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b9dbb9c52862ac974003241d68fb61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb4828b16c8e845492f1a53ddd9a9.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2b280a6a65c9bf2f20cad5d1106080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff60dcf2b1b2484b1ba940af96d336c.png)
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2021-05-30更新
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3卷引用:福建省永春一中、培元中学、石光中学、季延中学2024届高三下学期第二次联合考试数学试题