1 . (1)已知a,b,x,y均为正数,求证:
并指出等号成立的条件;
(2)利用(1)的结论,求函数
的最大值,并指出取最大值时x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7381cf2d8df0ec7f569046d580d40a1f.png)
(2)利用(1)的结论,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b13d632379fbe54d0c957d1d14329e.png)
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2024-01-13更新
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409次组卷
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4卷引用:四川省绵阳市2024届高三二模数学(理)试题
2 . 已知正实数
、
、
、
.
(1)证明:
,并确定取等条件.
(2)证明:
,并确定取等条件.
![](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)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4412956c389f11bc0552df20ae481bbc.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443ee9ff09e42d3f9feee049abdee5bc.png)
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2023-08-25更新
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2卷引用:四川省成都市第七中学(高新校区)2024届高三上学期入学考试数学(理科)试题
名校
3 . (1)已知
,用比较法证明:
;
(2)已知
,用基本不等式证明:
,并注明等号成立条件;
(3)已知
,用反证法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2128a00f52af4427721f0ebba591daa.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a521891098b625f372ff648d110afe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d66530037e9ad08b11dfe515571f41.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937559aeec06323cde8861b17024fc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be100015cff38b6dfba5080fa94d128.png)
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解题方法
4 . 设不等式
的解集为
.
(1)求证:
;
(2)试比较
与
的大小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d5cab03c293e2c2b56e7be1bda567b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bca6fb9e5e25c0fcac557b7ea8e769e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebca3befdfa438ae6d4946cc66056af9.png)
(2)试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f2a8ea6c69b9133d29a4c9060e98f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ab32d054ab39addb162a79bc872a6c.png)
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2023-01-18更新
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84次组卷
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2卷引用:贵州省铜仁市2023届高三上学期期末质量监测数学(文)试题
名校
解题方法
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c346f985091b21335795988d0ad7b848.png)
(1)求不等式
的解集
;
(2)若
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c346f985091b21335795988d0ad7b848.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940adbf54e96ecb2bb2637e5f976a3b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27dd329517f0dd8f1d0dfade6138ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab92728b35ed5798e07a2b0095bfcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/151e41a1e26ba035e82121c09702cc24.png)
您最近一年使用:0次
解题方法
6 . 已知二次函数
过坐标原点,且对任意实数x都有
.
(1)求函数
的解析式;
(2)当
、
,且
时,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb43c1b89394f44c9d41a4cf8dc3dab.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05a1af3e8fcfa14f964dec6c7c6a8d5.png)
您最近一年使用:0次
名校
7 . (1)已知
,试比较
与
的大小;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98ddef21b1a9f6928b42ed0c7d773a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ff948329ca52b40e10a0f205adf932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47fbac3e5eba01fc3f9c1b1de971f906.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70a255bb1660ce97c6fcdb2d523880a.png)
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2022-10-22更新
|
420次组卷
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3卷引用:安徽省淮南市部分学校2022-2023学年高一上学期10月联考数学试题
安徽省淮南市部分学校2022-2023学年高一上学期10月联考数学试题黑龙江省哈尔滨市第三中学2023-2024学年高一上学期第一次验收考试数学试题(已下线)专题03 不等式与不等关系压轴题-【常考压轴题】
名校
解题方法
8 . (1)设
,
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知
,
,求证:
![](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/99a737185eb85ca24cf66409ce1e09bc.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/26324941773aadc326cdfd502491484e.png)
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9 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ac12138178cb539a9e1c8f77587038.png)
(1)证明:
;
(2)已知
,
,求
的最小值,以及取得最小值时的
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ac12138178cb539a9e1c8f77587038.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b105f9f5823220345fe86cb2fc21ab.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348aca26e61218d251581e21c1129a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa209b3fac4adb64d36b3a263be0af5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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2022-05-09更新
|
1200次组卷
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6卷引用:贵州省贵阳市2022届高三适应性考试(二)数学(文)试题
贵州省贵阳市2022届高三适应性考试(二)数学(文)试题贵州省贵阳市2022届高三适应性考试(二)数学(理)试题(已下线)押全国卷(理科)第23题 不等式选讲-备战2022年高考数学(理)临考题号押题(全国卷)(已下线)专题03 等式与不等式的性质(已下线)专题03 等式与不等式的性质-2四川省成都市郫都区2024届高三上学期阶段检测(二)文科数学试题
名校
10 . 已知a,b,
.
(1)若
,求证:
;
(2)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0097ca400d4619a94c4282c1ef6ec68e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3aec1994a01be9e9335a62177131ee4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f9223bc24df8d429d743692fff7c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0818daf1a57c4b4c3666d411dcc76f8a.png)
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2022-04-07更新
|
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4卷引用:云南师范大学附属中学2022届高三高考适应性月考卷(九)数学(理)试题