名校
解题方法
1 . 已知为两条异面直线,
为平面,且
,
,
.
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15234cbaac1f69fabb0abebda7709092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5761a99d102beff950627c9b6c8e66d.png)
(2)用反证法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b330d69a949d9b55f4b6f18f47e0a37.png)
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2024-01-14更新
|
95次组卷
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4卷引用:上海市七宝中学2021-2022学年高二上学期期中数学试题
上海市七宝中学2021-2022学年高二上学期期中数学试题上海市南洋模范中学2021-2022学年高二上学期12月月考数学试题(已下线)专题03直线与平面的位置关系(4个知识点6种题型)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(沪教版2020必修第三册)(已下线)第四章 立体几何解题通法 专题一 反证法 微点2 立体几何中的反证法(二)【培优版】
2 . (1)已知
,试用分析法证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b1411bbc505b5056e68e077d18e06b.png)
(2)等差数列
中,已知
,试求n的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6c5526947e9bef051bc3bdf7fd186d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b1411bbc505b5056e68e077d18e06b.png)
(2)等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342ead1007636d0f9aed521b7bc73779.png)
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3 . (1)用综合法证明:设a,b均为正实数,且
,则
;
(2)试比较下列各式的大小(不写过程):①
与
;②
与
;通过上式请你推测出
与
(
且
)的大小,并用分析法加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98941347dd7ac01f5e63a6c5930dd5fa.png)
(2)试比较下列各式的大小(不写过程):①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d37b9f0421c90b1033dae9e3362c8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d1df3af8b2e212bc6d114959139823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d1df3af8b2e212bc6d114959139823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5246364ca8d76ddd707a001fe98cbb5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4457e63251cc30112b0146f99e71eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e5ca35ca665d421c919c97601539bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
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2023-02-04更新
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2卷引用:河南省郑州市励德双语学校2021-2022学年高二下学期第一次月考数学(理)试题
4 . (1)求证:
;
(2)若方程
和
中至少有一个方程有实数根,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376853ee76347b32132a8a7feedbf973.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589dc3fa67706f47d229e0778d901793.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bab67a391ba2678e91073f442b26425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
5 . 已知
∈(0,+∞),
若
求证:
中至少有一个数不大于1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec99c57bf7997bd93e1ed8f48d5af9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2f928fe46365cfb7cb905a12d0583a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77727464637f7e5ca2528c2450c4c08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec99c57bf7997bd93e1ed8f48d5af9a.png)
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6 . (1)用综合法证明:已知a,b,c都是实数,
;
(2)用分析法证明:对于任意a,
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718baee4ebadc334bb21aa4898ee72b9.png)
(2)用分析法证明:对于任意a,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57e3aae0913a02658df0f67ba8c126c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd5fc9df715d87bb7646d066f845563.png)
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2022-07-15更新
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145次组卷
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2卷引用:广西河池市2021-2022学年高二下学期期末考试数学(文)试题
7 . (1)设实数
、
、
成等比数列,非零实数
、
分别为
与
、
与
的等差中项.求证:
;
(2)三角形
的三边
、
、
的倒数成等差数列,求证:
.
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79e66286858d0890e324f63b698c39f.png)
(2)三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/dc74ad5dbb6029f4bd4ea0d52f576945.png)
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8 . (1)已知x>0,y>0,
,求证:
.
(2)a,b,
,求证:
,
,
不能都大于1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128294be1f10b83df30ad60d4c696224.png)
(2)a,b,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c415b871cbdc3215c1eacf1ed11dae6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d15cd3a09a5b2b7caebab7dd96852533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8d46fedbb81f3db10b826257b88912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e78bb8432a969c5d89bdd628501fd56.png)
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2022-06-02更新
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3卷引用:江西省吉安市安福二中、井大附中、吉安县三中、遂川二中2021-2022学年高二下学期四校联考(第三次月考)数学(文)试题
9 . 用综合法或分析法证明以下问题:
(1)若
是互不相等的实数,且
,求证:
.
(2)已知
.求证:
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa4b450e9269a7ef67582e7359f0125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b2d4c175ae8fadf2da3078ec2904d4.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd185d0e487fab58f8b0bfbb46e4ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba77de7002cfcd4ae007a3c8b813e3b0.png)
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2022-05-12更新
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2卷引用:陕西省宝鸡市金台区2021-2022学年高二下学期期中理科数学试题
10 . 求证:
(1)已知
,求证:
;
(2)已知a>0,b>0,且
,求证:
与
不可能同时成立.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae41b4ea7f44a8699f108def4a22ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f4fa6828188864939832ab3c23197a.png)
(2)已知a>0,b>0,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7dec5f5ef4a53175966c1704ad8a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656cacf9b32ce8f718dcb50bc8994593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f678dde8a2f44b8eae985b11bf4b50.png)
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2022-05-02更新
|
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2卷引用:江西省景德镇一中2021-2022学年高二下学期期中考试数学(文)试题