名校
1 . 给定无理数
.若正整数
,
,
,
满足
.
(1)试比较三数
,
,
的大小;
(2)证明存在两组不完全相同的正整数a,b,c,d满足
且
;
(3)若
,证明下面三个不等式中至少有一个不成立
①
②
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a3bc7f9c1aab24a770e989c5f924e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4710d3e509da892b6545d78e8f422a2.png)
(1)试比较三数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b207782857715994fcd5b2826bb5da7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45a8e3c0c4510ae1e7752a6ddc3dcce.png)
(2)证明存在两组不完全相同的正整数a,b,c,d满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4710d3e509da892b6545d78e8f422a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ca6053a889751a9ad6cef99b6916c3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ca6053a889751a9ad6cef99b6916c3.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d64363ccfd12cf4d17b50cc7d59e459f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c00d320136453c0093128550b7e50096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fda4b8f1f5f6c04554c2994c04f4345.png)
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2022-11-14更新
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3卷引用:上海市嘉定区第一中学2023-2024学年高一下学期5月月考数学试卷