名校
解题方法
1 . (1)已知
,
,
,证明:
;
(2)证明:当
,
时,有
.
![](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/131ac7eb1e911c9a40e84235bf3742ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743521dbdd63eb1ccda627d0f695db05.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c84b49231d0344d0813a7bbd2acdaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14a2671cb729ab8919ad06008671d69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49236cb8b41994a11aee4998576dd48.png)
您最近一年使用:0次
名校
2 . (1)已知:有理数都能表示成
(
,且
,
与
互质)的形式,进而有理数集
,且
,
与
互质
.
证明:(i)
是有理数.
(ii)
是无理数.
(2)已知各项均为正数的两个数列
和
满足:
,
.设
,
,且
是等比数列,求
和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0be44077d42cfffece905b1af13e000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e040fd7ed69d64faa73e837de9cf34da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b2400d72b1e3145cb21ba719d8a968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78fafccf5b7f9a2274588a3e0d53e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b2400d72b1e3145cb21ba719d8a968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167efd4154b88cb7d4f98a60db23b7f5.png)
证明:(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a78c6231e3700c9318da26652ffc3b4e.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
(2)已知各项均为正数的两个数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d29b427b203f5a022e32ed32e22e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7448f80a323b18d9071aafd1843d76b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
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2024-01-03更新
|
242次组卷
|
2卷引用:广东省中山市第一中学2024届高三上学期第五次统测数学试题
名校
解题方法
3 . 选用恰当的证明方法,证明下列不等式.
(1)已知
均为正数,且
,求证:
;
(2)已知
,求证:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/984faa7ae8bb62ce8157b0b60dc84508.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e10cc5dd849caccce37fe98a26c598.png)
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4 . 若
,
且
,则下列不等式中恒成立的是( )
![](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/cbe0890043f34b4575bf7bb3a773e32b.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
5 . 若正实数
,满足
,则下列不等式恒成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45900deae0489e87fe448948e8091c4.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-12-23更新
|
328次组卷
|
3卷引用:山西省大同市第一中学校2023-2024学年高一上学期12月月考数学试题
解题方法
6 . (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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7 . 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)
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名校
解题方法
8 . 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
|
319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】
名校
9 . (1)已知
,求
的取值范围;
(2)设a,b,c均为正数,且
,证明:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afba78f1ed058a450f2f74665ad7b150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd927b4b5a7875528c1b54aa4bb8b2dd.png)
(2)设a,b,c均为正数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d689b0da0bd4803b3e8a6c69542ae466.png)
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解题方法
10 . (1)已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a9344f4fca7b9779ca7720e5277ea6.png)
且
,求
的最小值.
(2)已知
,
,且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a9344f4fca7b9779ca7720e5277ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86db1ff1b996e33de049889c04bf9a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd31dc2d0967db352574381d66d33fc0.png)
(2)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/4a7dbc702617c765a573961953cc0901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054d00a127a585f7401a05d5351c6e37.png)
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