2023高一·上海·专题练习
1 . 设
,
,
是由三个整数组成的非空集,已知对于1、2、3的任意一个排列i、j、k,如果
,
,则
,证明:
,
,
中必有两个集合相等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0579e226c924b11043c7f5301cb9557e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036cde24aee4c56ce722aaffce48e520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/229ed0001e0265c506b51695b136bf71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
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2 . 已知椭圆E:
的右焦点为F,过F作互相垂直的两条直线分别与E相交于A,C和B,D四点.
(1)四边形ABCD能否成为平行四边形,请说明理由;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
(1)四边形ABCD能否成为平行四边形,请说明理由;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9de46dfa2b66a9ea3db7e9e186fcd9c.png)
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