名校
1 . (1)已知:有理数都能表示成
(
,且
,
与
互质)的形式,进而有理数集
,且
,
与
互质
.
证明:(i)
是有理数.
(ii)
是无理数.
(2)已知各项均为正数的两个数列
和
满足:
,
.设
,
,且
是等比数列,求
和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0be44077d42cfffece905b1af13e000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e040fd7ed69d64faa73e837de9cf34da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b2400d72b1e3145cb21ba719d8a968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78fafccf5b7f9a2274588a3e0d53e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b2400d72b1e3145cb21ba719d8a968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167efd4154b88cb7d4f98a60db23b7f5.png)
证明:(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a78c6231e3700c9318da26652ffc3b4e.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
(2)已知各项均为正数的两个数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d29b427b203f5a022e32ed32e22e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7448f80a323b18d9071aafd1843d76b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
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2024-01-03更新
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2卷引用:广东省广州市广东实验中学2024届高三上学期大湾区数学冲刺卷(三)
名校
解题方法
2 . 已知正数
满足
.
(1)若
,求
的最小值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6054a344e7a525f65b1344ecf222529.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980ab4deb9e7f2bc9288787f5243a4d2.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/844435b1ad835a082e6b15fbbea0678c.png)
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2023-12-21更新
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319次组卷
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3卷引用:名校教研联盟2024届高三上学期12月联考(全国卷)数学(理)试题
名校教研联盟2024届高三上学期12月联考(全国卷)数学(理)试题陕西省榆林市十校2024届高三上学期12月联考数学(文)试题(已下线)考点7 基本不等式及其应用 --2024届高考数学考点总动员【练】
解题方法
3 . 设a,b,c为正实数,且
.
(1)证明:
.
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be94bcdd073e5e6c8137caa90e41b9a.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7a3cf29f7500c49b8df17279cdc431.png)
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2023·全国·模拟预测
4 . 已知
,且
.
(1)求证:
;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2133cd64cdc27fb7b1784f05887f7304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeadd667059ca5e53125d3c0cda85bae.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131c6728de06c3c67cd2d8dba0a7fde6.png)
您最近一年使用:0次
2023·全国·模拟预测
5 . 已知正数
,
,
满足
,证明:
(1)
.
(2)
.
![](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/3fd9e365eec43d1200ee1d5a0b559ee3.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c79bb1871fa70b9796f41dacde13bd0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e644b5ea232a501c2ee7c1b4e2d41d19.png)
您最近一年使用:0次
2023·全国·模拟预测
6 . 已知a,b,c均为正数,且
,证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42d412d5a5c13e17ebc05ad19c098b2.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5567c73aead91151f22c3a83aa0f2092.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/750323a94254a8658d70da105241ef2c.png)
您最近一年使用:0次
2023·全国·模拟预测
7 . 已知x,y,
.
(1)若
,证明:
;
(2)若
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588e4cf838add469512e328d2e60916b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58fb952f9a33887a3f80b04e1e5e6134.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeadd667059ca5e53125d3c0cda85bae.png)
您最近一年使用:0次
名校
解题方法
8 . 已知
,若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd98ce07e05c58d83a48d90dfcb28fd2.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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2023-11-13更新
|
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3卷引用:海南省部分学校2024届高三上学期学业水平诊断(一)数学试题
海南省部分学校2024届高三上学期学业水平诊断(一)数学试题山西省临汾市2023-2024学年高三上学期11月期中数学试题(已下线)专题03 不等式与基本不等式的应用(3大易错点分析+解题模板+举一反三+易错题通关)
名校
解题方法
9 . 已知
,
,且
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f00f997ae12c30f551adb834e1d7ef8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7卷引用:山东省临沂市兰陵县第一中学2024届高三上学期教学质量检测模拟考试(11月校际联考)数学试题
名校
解题方法
10 . 若
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/867a52232899b0a2222d72a63e0727a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8db23a45150db6e92d58e01e8b287c5.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4卷引用:云南省大理白族自治州大理市辖区2024届高三区域性规模化统一检测数学试题
云南省大理白族自治州大理市辖区2024届高三区域性规模化统一检测数学试题云南省三校2024届高三高考备考实用性联考卷(三)数学试题福建省福州格致中学2024届高三上学期期中考试数学试题(已下线)考点7 基本不等式及其应用 --2024届高考数学考点总动员【讲】