名校
解题方法
1 . 柯西不等式具体表述如下:对任意实数
,
,
和
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
,
都有
,当且仅当
时取等号.
(1)请用柯西不等式证明:对任意正实数
,
,
,
,不等式
成立,(并指出等号成立条件)
(2)请用柯西不等式证明:对任意正实数
,
,
,
,且
,求证:
(并写出等号成立条件).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09356b015bc795d6d54cd3ba4078b265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c254ae1c29768fed8c7f9a14d52395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de74ebc1d7d0ef4f23c30ecdddbb9a7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c54ff21406dc68cdab0d21351daf51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b90c1b5ccde843b2e8fea459376247.png)
(1)请用柯西不等式证明:对任意正实数
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29574517e0bd98aa055ee15120f8fff1.png)
(2)请用柯西不等式证明:对任意正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b16ad49f62d7362441e3b92efe7f87d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b3d6d2614a5cdbddc5964194a1a925.png)
您最近一年使用:0次
名校
解题方法
2 . 设
,
,
均为正数,且
1.
(1)求
的最小值;
(2)证明:
.
![](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/892560dcff6af9f66a3f735652f69dd7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57f879f6e8df7d5fb261328806260b3.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08b8a4fc07b2dda2b5cf21314411936.png)
您最近一年使用:0次
2022-06-29更新
|
681次组卷
|
5卷引用:陕西省西安市碑林区2022-2023学年高一上学期期中联考数学试题
陕西省西安市碑林区2022-2023学年高一上学期期中联考数学试题陕西省西安市西北工业大学附属中学2022-2023学年高一上学期期中数学试题江西省南昌市八一中学2021-2022学年高二下学期期末考试数学(理)试题内蒙古呼伦贝尔市满洲里市第一中学2021-2022学年高二下学期期末考试数学(理)试题(已下线)专题2.9 一元二次函数、方程和不等式全章综合测试卷-提高篇-2022-2023学年高一数学举一反三系列(人教A版2019必修第一册)
名校
解题方法
3 . 1.已知函数
.
(1)若关于x的不等式
的解集不是空集,求实数a的取值范围;
(2)设
,
,且
,求证:对任意给定的满足条件的实数m、n,总有不等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd6302c1fc18c859e7f15a5ed7853e5.png)
(1)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4aa539556add14df9b3fc68b9827464.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ad5cfb7effa1c06226413e2bc49d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abbfa7d2e01b7641aedf8611408449e.png)
您最近一年使用:0次
2021-11-09更新
|
454次组卷
|
2卷引用:上海市复兴高级中学2021-2022学年高一上学期期中数学试题