名校
解题方法
1 . 若
,
,
,则对一切满足条件的
,
恒成立的有( )
![](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/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-10-14更新
|
140次组卷
|
2卷引用:江苏省南京市第一中学2023-2024学年高一上学期10月学情调研测试数学试题
名校
解题方法
2 . 选用恰当的证明方法;解决下列问题.
(1)
为实数,且
,证明:两个一元二次方程
,
中至少有一个方程有两个不相等的实数根.
(2)已知:
,且
,求证:
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1476efe1fd8970d815af8a6e62d454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341f6b48e2c616585ed9bd7dbb9c8728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3ce04492780c4d40fab17aa28d3755.png)
(2)已知:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c96a416540d6d2c2570c7106f5e0492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03f1c0c0618a585e86afc523bd523e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356bc29ee1bc3f046d9a7b2804c77cf9.png)
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2023-10-14更新
|
97次组卷
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2卷引用:辽宁省大连市金州区金州高级中学2023-2024学年高一上学期10月月考数学试题
名校
解题方法
3 . 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)
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2023-10-14更新
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239次组卷
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5卷引用:山东省2023-2024学年高一上学期“选科调考”第一次联考数学试题
名校
4 . 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)
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5 . (1)
为实数,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f25298d03745e6d91799449ed9e96a.png)
(2)用分析法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f25298d03745e6d91799449ed9e96a.png)
(2)用分析法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b492c09f576ab6491af4848ce7ecec4.png)
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名校
解题方法
6 . 解答下列各题.
(1)已知
,试比较
与
的大小;
(2)设
均为正数,且
,证明:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca24341509c05e672999202f2df0ebaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/444b88d2de0c2e06f5efae2578e3ef8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef758c8f9983a4dacaaa1eed75ad455.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b09fc94ae8293ad1de55d2990502588e.png)
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7 . 已知
,且
都是正数.
(1)若
,求证:
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a6f362a7f8f972d6b329a882e940d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba9c88a847d8483a887b088159c7c0f1.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f917a19a15bceb9a3769e59e25dd9c.png)
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名校
解题方法
8 . 已知
为正实数.
(1)若
,求
的最小值;
(2)若
,试判断
与
的大小关系并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd98ce07e05c58d83a48d90dfcb28fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57f879f6e8df7d5fb261328806260b3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28f616b1f56991ee75caae3ac35208b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c219195fb02ac624820d0f37a3b7fa46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaab99cc8dd6ebc1de807a1d5e3c6d5.png)
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9 . 已知集合
的子集个数为
.
(1)求
的值;
(2)若
的三边长为
,证明:
为等边三角形的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ce22a79915802052a731ea4eb70a1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8858e7b26a1860f4c4e0da7da33bbada.png)
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2023-10-13更新
|
136次组卷
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8卷引用:江西省部分学校2023-2024学年高一上学期10月联考数学试题
解题方法
10 . 已知正数a,b满足
;
(1)求ab的最大值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0d34836cf6d21bcadd4f60793ba150.png)
(1)求ab的最大值;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296a77a7ca3e70fba643654bf5a99a3b.png)
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2023-10-12更新
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349次组卷
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5卷引用:陕西省部分学校2023-2024学年高一上学期10月选科调考数学试题