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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21-22高一·湖南·课后作业
2 . 下列结论是否成立?若成立,试说明理由;若不成立,试举出反例.
(1)若
,则
;
(2)若
,则
;
(3)若
,则
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d5f0d374837655cc286d326305da36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759c09917e5728d75bf5cfdb5b4a807f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d5f0d374837655cc286d326305da36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5761e8fbc832afcfce07dab1d4dfc385.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed37ee7432002cd0e0978b2012e184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37006891004d02050e7c57db20af3981.png)
您最近一年使用:0次
21-22高一·湖南·课后作业
解题方法
3 . 证明下列不等式,并讨论等号成立的条件:
(1)若
,则
;
(2)若
,则
;
(3)若
,则
;
(4)若
,则
;
(5)对任意实数
和
,
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d87d567e5ccc0d31d063609810e5cc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a655d6935ae3f646e17ff72bc213e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b20f398d8772984301018f832966b14.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6343069217cd6d8dd32446da428dae46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f23c87e770c3cc61bad09643926ae6.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eae9ba258299eb489b490594397e23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46973ec354692c420913269bc23a8035.png)
(5)对任意实数
![](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/91a470f596a01c8273f55b9fb394b0f6.png)
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20-21高一·江苏·课后作业
4 . 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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5 . 已知
都是正数,且
.
求证:(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11a069688e4c797fcf527eab15afa82.png)
求证:(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2995d6c721ccbf993afe2c82a85eca.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0288a015d985d29ebfd58a982927bea.png)
您最近一年使用:0次
2020-08-08更新
|
2400次组卷
|
12卷引用:专题5 “课本典例”类型
(已下线)专题5 “课本典例”类型(已下线)第02讲 2.2基本不等式(1)-【帮课堂】(已下线)2.2 基本不等式(第1课时)(导学案)-【上好课】(已下线)对点练05 基本不等式-2020-2021年新高考高中数学一轮复习对点练(已下线)2.2 基本不等式(精讲)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第一册)(已下线)课时2.2 (考点讲解)基本不等式-2021-2022学年高一数学新课学习讲与练精品资源(人教版2019必修第一册)人教A版(2019)必修第一册课本习题2.2 基本不等式(已下线)2.2基本不等式【第一练】人教A版(2019) 必修第一册 逆袭之路 第二章 2.2 基本不等式(已下线)3.4+基本不等式(1)-2020-2021学年高二数学课时同步练(人教A版必修5)人教A版(2019) 必修第一册 新高考名师导学 第二章 2.2 基本不等式(已下线)2.2 基本不等式
6 . 已知
、
都是正数,求证:
(1)如果积
等于定值
,那么当
时,和
有最小值
;
(2)如果和
等于定值
,那么当
时,积
有最大值
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)如果积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f29d5f376c75c41ae6af0c8a8565449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b9d5aaaceaa3ac514d17fcfefbf9b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c772f4f867c7f3050601f1034b6f7e6.png)
(2)如果和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b9d5aaaceaa3ac514d17fcfefbf9b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f29d5f376c75c41ae6af0c8a8565449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dee9fc9dfc47bb7d18aa7c7a57b86e.png)
您最近一年使用:0次
2020-02-07更新
|
938次组卷
|
5卷引用:2.2 基本不等式(第1课时)(导学案)-【上好课】
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