名校
解题方法
1 . 已知
,
,
均为正数
(1)求证:
;
(2)若
,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)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8920a005c0b2e5b9cf0f916d1ce20329.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf43bd907a0590831d324d5eff38ea54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd71a22dc65b28a0e6f8e4b9ee9e3b0.png)
您最近一年使用:0次
名校
解题方法
2 . 设
为正数,且
. 证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d69582b1a383cda899bfae292812f69d.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c69ec969e81e98cc5051a1817ac866.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538f858f3a28c8faa69cb9463d619671.png)
您最近一年使用:0次
2024-05-13更新
|
279次组卷
|
2卷引用:陕西省西安市第一中学2023-2024学年高三下学期4月月考理科数学试题
名校
解题方法
3 . 已知
,当
时,不等式
成立.
(1)求
的最大值;
(2)设正数
,
的和恰好等于
的最大值,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18822a123bc80412508a309ef5dd7159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c67ddd60c47e91783929c8bdf8ba8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设正数
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16195724ab65f5ed0f378a14051ff5bd.png)
您最近一年使用:0次
名校
4 . 已知
,
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bbd0aae5a4f6129fc78f88f662f092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea134f599285e3d32d2ab3e7186990.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2024-03-10更新
|
1249次组卷
|
3卷引用:陕西省安康市高新中学2024届高三下学期3月月考数学(理)试题
解题方法
5 . (1)解不等式:
.
(2)已知
都是正数,求证::
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e03f5e2ce625506cc6901e3bbfd57616.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca946693693753e4b53403dfff80761.png)
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6 . 证明下列不等式
(1)已知
,
,
,且
,求证:
.
(2)已知
,
,
,求证:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.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/4cad3aaeb5b444feb152378278f68863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5cc7582a7b091b3f0f5a51325e1d0a1.png)
您最近一年使用:0次
名校
解题方法
7 . 已知正数
满足
.
(1)若
,求
的最小值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6054a344e7a525f65b1344ecf222529.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980ab4deb9e7f2bc9288787f5243a4d2.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/844435b1ad835a082e6b15fbbea0678c.png)
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2023-12-21更新
|
318次组卷
|
3卷引用:陕西省榆林市十校2024届高三上学期12月联考数学(文)试题
陕西省榆林市十校2024届高三上学期12月联考数学(文)试题名校教研联盟2024届高三上学期12月联考(全国卷)数学(理)试题(已下线)考点7 基本不等式及其应用 --2024届高考数学考点总动员【练】
8 . 已知
,
,
,求证:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9637478a4b3023e608a6ac08ce9d6ffe.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c8db91a42a1f487bee8f12ea9d67fc1.png)
您最近一年使用:0次
名校
解题方法
9 . 已知正数
,
满足
.
(1)求
的最小值;
(2)若正数
满足
,证明:
与
之和为定值,且
.
![](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/5be97cd1c7111b654d87d8fbb63b6a84.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e29dbe0f9a9c78de90afcfc2ea96a5.png)
(2)若正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6057c1f4d6840d9a3e5021d63621519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1810555c0c28fe352841322b85bbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2ed49b4be25eac88aa2af01aa84c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665be0848dec4920536fd38af1f67063.png)
您最近一年使用:0次
2023-10-14更新
|
242次组卷
|
5卷引用:陕西省西安市庆安高级中学2023-2024学年高一上学期第一次月考数学试题
名校
10 . 已知a,b为正实数.
(1)若
,求证:
;
(2)若
,求证:
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89dc8118d95d6c7bd5b7d38667a498e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485a2d99320384a0857b00ce9ab9e990.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d1c23264891eb9cfda0691334e5d43.png)
您最近一年使用:0次