21-22高一·湖南·课后作业
解题方法
1 . 证明不等式:
(1)若
,
,
,
都是正数,求证:
;
(2)若
,
,
是非负实数,则
;
(3)若
,
是非负实数,则
;
(4)若
,
,则
.
(1)若
![](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/d2e7387a3fbab6508695365955f55258.png)
(2)若
![](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/b2d92a6b95fdfdedb405447340293bdc.png)
(3)若
![](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/727ff3ac24b506706045956c16336f94.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f58b9bc974b789928f6490acb43fb3.png)
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20-21高一·江苏·课后作业
解题方法
2 . 证明下列不等式:
(1)
;
(2)
;
(3)若a,
,则
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe4d5d2659300ca5539f228fab5e4d7.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0defbce6e08542fbcf1f527a6d8cd85.png)
(3)若a,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a8f4f4b9a63a58c3a4b53bd5b770d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59fdaf498ee257fd1ab3f8e7416fce5.png)
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20-21高一·江苏·课后作业
3 . 证明:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65ea68f7337a3704478bae1adc9f4485.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300e7ed73ebe7fa5cff9c6927995a848.png)
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20-21高一·江苏·课后作业
名校
4 . 如图,
为梯形,其中
,
,设O为对角线的交点.
表示平行于两底且与它们等距离的线段(即梯形的中位线),
表示平行于两底且使梯形
与梯形
相似的线段,
表示平行于两底且过点O的线段,
表示平行于两底且将梯形
分为面积相等的两个梯形的线段.
,
,
,
与代数式
,
,
,
之间的关系,并据此推测它们之间的一个大小关系.你能用基本不等式证明所得到的猜测吗?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520f8abda6a85e7ef6f281fc2df853fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d42e97eee705d164e6ac6de9ecd6d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0786732df29e599cd67cd69e5a1a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae57e49b519bb89ea02274318a34438d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d9a39b4dab211a19ee2950a93c7049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59000198fc5779f7ecf141860ff08a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520f8abda6a85e7ef6f281fc2df853fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae57e49b519bb89ea02274318a34438d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f89a8b5cf6996a6455375e405bfb9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d7009d4cbe7157d63ce50444443716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4dda7369edf57a39cfad583031328a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc8b26fb79c1f4d36130c41b18c0f9c.png)
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2021-10-30更新
|
248次组卷
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5卷引用:第三章本章回顾
(已下线)第三章本章回顾江苏省连云港高级中学2023-2024学年高一上学期第一次学情检测数学试题苏教版(2019)必修第一册课本习题第3章复习题(已下线)第二章 一元二次函数、方程和不等式(压轴必刷30题4种题型专项训练)-【满分全攻略】(人教A版2019必修第一册)湖北省荆门市东宝中学2023-2024学年高一上学期期中数学试题
20-21高一·江苏·课后作业
5 . 设a,b,c,d为实数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ed1405c966de67e49e7f241d67a8d87.png)
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20-21高一·江苏·课后作业
6 . 证明:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6e89ff670f9a10eb087a02051f3a50.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c573bd16158492f3c6533261d2188b.png)
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20-21高一上·全国·单元测试
7 . 已知a,b都是正数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94ef18a34a8f1a1bc46cb2d431a36cf.png)
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2020-08-27更新
|
390次组卷
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5卷引用:3.2 基本不等式
(已下线)3.2 基本不等式(已下线)专题2.1不等式及基本不等式(A卷基础篇)-2020-2021学年高一数学必修一同步单元AB卷(人教A版浙江专用)第二章 等式与不等式 2.2 不等式 2.2.3均值不等式及其应用人教B版(2019)必修第一册课本习题2.2.4 均值不等式及其应用苏教版(2019)必修第一册课本习题 习题3.2