1 . 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)
您最近一年使用:0次
2022-05-02更新
|
118次组卷
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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
2 . (1)用综合法证明:已知
、
、
都是实数,
.
(2)用分析法证明:对于任意
、
,都有
.
![](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/340a7d19c931c620194ed69ca85d9b03.png)
(2)用分析法证明:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826e907db02eff4c979278b3eee7cc29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf93fca1840aefafcebb38fa81a18dba.png)
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2022-04-22更新
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194次组卷
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2卷引用:河南省洛阳市创新发展联盟2021-2022学年高二下学期联考(三)数学(文科)试卷
名校
3 . 证明:
(1)若
,则
;
(2)求证:当
为正数时,
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ad6cf9fb725f7947bddaf3149ba07d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca34726fb86e4bdeeb4e87778148bf3.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43545d069f7d7c5f87bfdcad4ce63801.png)
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2022-04-08更新
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2卷引用:河南省豫北名校2021-2022学年高二下学期4月份教学质量检测理科数学试题
4 . 已知函数
,
、
为两个正实数.
(1)若
,求证:
、
中至少有一个不小于
;
(2)若
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ef684160352e0bc0719773cbf01d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45609ff2c5ef5f618f706eed7b88dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f484115a9df1b6060d6b14df85c6f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35770a47ffcba6bf1d94eceabb416d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba934874cc9f2ab272fdff67ea23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d8b93ecbaab8a7a4899a042399f5fb.png)
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名校
解题方法
5 . (1)a,b,
,求证:
,
,
不能都大于1.
(2)已知
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa7b9037d62bde0a2fca3f7da9fc351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9b76fc410e367b02fa2e146ba2d854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f280f0ed2cae448ba4791f1849b0028d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8b33232aca52c3f4bbaa4f37ec227cb.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128294be1f10b83df30ad60d4c696224.png)
您最近一年使用:0次
名校
6 . 证明:
是无理数.(我们知道任意一个有理数都可以写成形如
(m,n互质,
)的形式)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b37b5491ba51f9d3e7842491cd8ae9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb60d38020a8a7afcef36a456b9b54b3.png)
您最近一年使用:0次
名校
7 . 已知a,
,证明:
,
,
这三个数中至少有一个大于或等于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e57c41567ce6b4aa3bfbba3b4a197d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f2a5b2645fd86840ceaa3d67796a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/935e804e4ad39ce11d593a90befed5c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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2022-03-24更新
|
155次组卷
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4卷引用:河南省2021-2022学年高二下学期联考(二)文科数学试卷
名校
8 . 设a,b,c均为正数,则
,
,
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f8122ee10aa2122a91e08d8d6d350d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75211eb335491ac5bf72459a80b5728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eecded67415b0848f3c23c1a8e2f741.png)
A.都不大于6 | B.都不小于6 |
C.至多有一个不大于6 | D.至少有一个不小于6 |
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10卷引用:安徽省六安市第一中学2018-2019学年高二下学期第一次段考数学(理)试题
安徽省六安市第一中学2018-2019学年高二下学期第一次段考数学(理)试题陕西省榆林市第十二中学2020-2021学年高二下学期第一次月考理科数学试题河南省2021-2022学年高二下学期联考(二)文科数学试卷河南省2021-2022学年高二下学期联考(二)理科数学试题河南省中原好教育联盟2021-2022学年高二下学期第二次联考数学理科试题河南省中原好教育联盟2021-2022学年高二下学期第二次大联考文科数学试题江西省抚州市七校2021-2022学年高二下学期期末考试数学(理)试题江西省抚州市七校2021-2022学年高二下学期期末考试科数学(文)试题陕西省延安市第一中学2021-2022学年高二下学期期中文科数学试题上海市进才中学2023-2024学年高一上学期期中数学试题
解题方法
9 . 设
,
,则下列不等式中不是恒成立的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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10 . (1)
;
(2)设
,用综合法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2004c4efdb09b151bb1018bb9f36b9c3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ada798eeba5bd19d497bfd0741afd00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
您最近一年使用:0次
2021-11-01更新
|
453次组卷
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2卷引用:甘肃省平凉市静宁一中普通班2020-2021学年高二下学期第一次月考数学(文)试题