1 . 对于三元基本不等式请猜想:设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec197b8ab457cfee3d4733f3d7f8d6f3.png)
_________ ,当且仅当
时,等号成立(把横线补全).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec197b8ab457cfee3d4733f3d7f8d6f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44acc0ee22dc4b7750e8be825e7c1355.png)
您最近一年使用:0次
2 . 我们学习了二元基本不等式:设
,
,
,当且仅当
时,等号成立利用基本不等式可以证明不等式,也可以利用“和定积最大,积定和最小”求最值.
(1)对于三元基本不等式请猜想:设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d682a527649f63b786d3f3706dc6b11d.png)
当且仅当
时,等号成立(把横线补全).
(2)利用(1)猜想的三元基本不等式证明:
设
求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d57d75f62befa523a65edaecfcdb44.png)
(3)利用(1)猜想的三元基本不等式求最值:
设
求
的最大值.
![](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/689f982af451283289255c87593ec338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
(1)对于三元基本不等式请猜想:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d682a527649f63b786d3f3706dc6b11d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e119c508fd265e3e3d78749e54fe4f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44acc0ee22dc4b7750e8be825e7c1355.png)
(2)利用(1)猜想的三元基本不等式证明:
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04275b84329feb739a9d6a03d3247491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d57d75f62befa523a65edaecfcdb44.png)
(3)利用(1)猜想的三元基本不等式求最值:
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f51064c8db93d090c963ca17743ee9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddd7de06ce423eaed2f95780cac0a1c.png)
您最近一年使用:0次
2019-11-03更新
|
437次组卷
|
3卷引用:山东省泰安市第四中学2019-2020学年高一上学期第一次月考数学试题
山东省泰安市第四中学2019-2020学年高一上学期第一次月考数学试题(已下线)2.2.2 基本不等式的应用(课时作业)-2020-2021学年上学期高一数学同步精品课堂(新教材人教版必修第一册)2023版 湘教版(2019) 必修第一册 过关斩将 第2章 综合拔高练
名校
解题方法
3 . 有下列命题:
①不等式
的解集为
;
②若
,函数
的最小值是2;
③对于
,
恒成立,则实数
的取值范围是
;
④已知
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7c299ac496c0fb85c77eacab348e22.png)
,若
是
的充分不必要条件,则实数
的取值范围是
.
其中真命题的序号为________________ .(把所有正确答案的序号填写在横线上,多选、错选不给分)
①不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5d21732d8a22de752d615b46867f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796daaf8d1d5ebeab2d0d989dffe3716.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647e17f9be50dcaba45fa6b15d5d982a.png)
③对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b78b09b0bae2d4e347a8445393ac19f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8c8fd3bdee0551dd6048a131f9eeb7.png)
④已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b964e01f15a297b8cc3cb564dea1cf01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7c299ac496c0fb85c77eacab348e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9cd3690e7aa3debb1ed054a9f622da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d54209e68b27ab4c59f51aa1e6f3d6fd.png)
其中真命题的序号为
您最近一年使用:0次
名校
解题方法
4 . 《几何原本》中的几何代数法是以几何方法研究代数问题,这种方法是后西方数学家处理问题的重要依据,通过这一原理很多的代数公理或定理都能够通过图形实现证明,也称之为无字证明,现有图形如图所示,C为线段
上的点,且
,
,O为
的中点,以
为直径作半圆,过点C作
的垂线交半圆于D,连接
,
,
,过点C作
的垂线,垂足为E,若不添加辅助线,则该图形可以完成的所有无字证明为__________ .(填写序号)
①
;②
;
③
;④
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3d296e0d7154a170cb7d3ae42989b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a88b719166fcc1431f876bc8c5656c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/3829f1ef-4d36-4411-b991-19beda49ad27.png?resizew=169)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb90c316d8a99694396de80ed0b0cf25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09adf1ac3103c5ddfe7a92856cb2afbe.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf323321cd5f80e909c243941c33f7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a305a51783a797bdda25197e090feb05.png)
您最近一年使用:0次
名校
解题方法
5 . 李老师在黑板上写下一个等式
,请同学们在两个括号内分别填写两个正数,使得等号成立,哪个同学所填的两个数之和最小,则该同学获得“优胜奖”.小明同学要想确保获得“优胜奖”,他应该在前一个括号内填上数字________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/713a7363b4ea3c93853b62a5bcd5cdb1.png)
您最近一年使用:0次
2023-01-16更新
|
288次组卷
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5卷引用:江苏省宿迁市沭阳县2020-2021学年高一上学期期中数学试题
名校
6 . 《几何原本》中的几何代数法是以几何方法研究代数问题,这种方法是后西方数学家处理问题的重要依据,通过这一原理很多的代数公理或定理都能够通过图形实现证明,也称之为无字证明,现有图形如图所示,
为线段
上的点,且
为
的中点,以
为直径作半圆,过点
作
的垂线交半圆于
,连结
,过点
作
的垂线,垂足为
,若不添加辅助线,则该图形可以完成的所有无字证明为_________ .(填写序号)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/515a8637-30c5-4728-85f4-0240e20f3913.png?resizew=161)
①
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7009eee373cc98ef7c8243901ec83037.png)
③
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ff0b118e5145f94c90c975e1fb74ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20740df2f6ae49f8dc88d2449897f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/515a8637-30c5-4728-85f4-0240e20f3913.png?resizew=161)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4d4e4d991871f2f35309b1604c9fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7009eee373cc98ef7c8243901ec83037.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8378bcf7139202d78b706b726602caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39dce2a6f257ad000947a4261da9783.png)
您最近一年使用:0次
2023-02-02更新
|
476次组卷
|
5卷引用:上海市南洋模范中学2021-2022学年高一上学期期中数学试题
7 . 在下列命题中,正确的命题有__________ .(填写正确的序号)
①若
,则
的最小值是6;
②如果不等式
的解集是
,那么
恒成立;
③设
,且
,则
的最小值是
﹔
④已知两非零向量
与
的夹角为120°,且
,
,则
;
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92029b9a53d88a72cc5ee653de6d03ed.png)
②如果不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae8fff7c98b78992edcd61daf6ea72f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7b2668d8fcf713370822c8e368ba7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da693578d4cd0c841fd529fe7ebfe4d.png)
③设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edae93ec9de65d7e8afd2a53063c8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8887f77124cbe18a4931826ede9c9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
④已知两非零向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7f14dfa9f463d57664c640102bb5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73ce450dda0622666af006f6865f8828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7e9a7c6bd5ba08238318a7c7df02c5.png)
您最近一年使用:0次
名校
解题方法
8 . 在下列命题中,正确的命题有________ (填写正确的序号)
①若
,则
的最小值是6;
②如果不等式
的解集是
,那么
恒成立;
③设x,
,且
,则
的最小值是
;
④对于任意
,
恒成立,则t的取值范围是
;
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92029b9a53d88a72cc5ee653de6d03ed.png)
②如果不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae8fff7c98b78992edcd61daf6ea72f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7b2668d8fcf713370822c8e368ba7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da693578d4cd0c841fd529fe7ebfe4d.png)
③设x,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2519954ec2deabecd7e057886fa4023c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8887f77124cbe18a4931826ede9c9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
④对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b687f97094676b2755bc724219a58520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ce220e0583c843810d4b44de111156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49bc53d70ee599df5cad39f06f728c2.png)
您最近一年使用:0次
2020-11-23更新
|
339次组卷
|
4卷引用:河南省郑州外国语学校2020-2021学年第一学期高二期中考试数学(理科)试题
河南省郑州外国语学校2020-2021学年第一学期高二期中考试数学(理科)试题(已下线)专题1.1 命题及其关系-2020-2021学年高二数学课时同步练(苏教版选修1-1)(已下线)专题1.1 命题及其关系-2020-2021学年高二数学课时同步练(苏教版选修2-1)山西省怀仁市2021-2022学年高一上学期期中数学(理)试题
解题方法
9 . 已知关于
的方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38abfe94aab2620c3f39e483615dfbf5.png)
有两个实根
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
,则下列不等式中正确的有______ .(填写所有正确结论的序号)
①
; ②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d991bd47bd0825b3a84f5d635ee5f9dc.png)
③
; ④
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38abfe94aab2620c3f39e483615dfbf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cea72e0c37257bcfd85a59ef8dd0f80.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/94ce41c1548ce8cfb04284ad9768878a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6175a72db472feeed10e44fd8df3fc70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d991bd47bd0825b3a84f5d635ee5f9dc.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6566566211b4627a3e2447c3d126ce7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00ea29ab2851b2b9585cb0a3225e560.png)
您最近一年使用:0次
2021-09-11更新
|
464次组卷
|
4卷引用:河南省大联考2021-2022学年高三上学期阶段性测试(一)文科数学试题
河南省大联考2021-2022学年高三上学期阶段性测试(一)文科数学试题河南省十所名校2021-2022学年高三上学期文科数学阶段性测试(一)(已下线)专题17 不等式-备战2022年高考数学学霸纠错(全国通用)(已下线)考向22不等式性质与基本不等式(重点) - 2
名校
10 . 下列命题正确的是________ .(填写正确的序号)
①在等差数列
中,有
,则
;
②已知数列
是正项等比数列,且
,则
的值可能是
;
③已知函数
是定义在R上的奇函数,且对任意
,都有
成立,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b6ed8cbd4162259985201ddfa4a049.png)
.
①在等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788beef99e78bcb25b193a0e50362d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c634e9a8afd9e6c931307dfaabb06810.png)
②已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3469ea4b3664ef316692458c96ac68d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
③已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
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2020-11-20更新
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2卷引用:江西省赣州市十五县(市)十六校2021届高三上学期期中联考数学(文)试题