1 . 已知
和数表
,其中
.若数表
满足如下两个性质,则称数表
由
生成.
①任意
中有三个
,一个3;
②存在
,使
中恰有三个数相等.
(1)判断数表
是否由
生成;(结论无需证明)
(2)是否存在数表
由
生成?说明理由;
(3)若存在数表
由
生成,写出
所有可能的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1b76c6898e230717d3daed334b0303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbda44091b0da7321b26722d6ab78845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac56300140ed9e27f8dff86ef1eaea0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c7d6627a568c6eaae35260d53dfb29.png)
①任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f29210b9144737a127a428679c58f406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd600b451b2b7f1680cbbcf36a49703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5137f97e66d136940d82a4027cd4fa2b.png)
(1)判断数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a97e4a4a351df2053a3cab244213d41c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e88b1329f12c3b53e86627d04f5e5a3.png)
(2)是否存在数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79dc44942df9856c903cd70e4776e86b.png)
(3)若存在数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0808a749c7fe9d45bea1edbd3ee96e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f44f67ab69be2217f7884536cfa53aa.png)
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2024-01-17更新
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6卷引用:辽宁省沈阳市第二中学2024届高三下学期开学考试数学试题
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