解题方法
1 . (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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2 . 已知
,
,且
,下列说法正确的是( )
![](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)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . (1)已知
克糖水中含有
克糖(
),再添加
克糖
)(假设全部溶解),糖水变甜了.这一事实可以表示为不等式
,证明这个不等式成立.
(2)已知
都是正数,求证
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d100c22435a23e017cfe6f535379d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a3a82d6b1b6ed16c30367f038c16bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac2bdea081bcd1c706cc82f906f226ce.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308b2921746b1ee3f499e220c371ca96.png)
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2023-11-07更新
|
102次组卷
|
2卷引用:新疆乌鲁木齐市实验学校2023-2024学年高一上学期第一次月考数学试题
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解题方法
4 . 下列结论正确的是( )
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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2023-10-30更新
|
117次组卷
|
2卷引用:江苏省镇江等地区联盟校2023-2024学年高一上学期10月调研数学试题
解题方法
5 . 已知正数a,b满足
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0d34836cf6d21bcadd4f60793ba150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296a77a7ca3e70fba643654bf5a99a3b.png)
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6 . (1)比较
与
的大小;
(2)已知
为不全相等的正实数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375fff2f7742a0010332e9f7add47f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30cf2063e96e2fec6c509dce6cad6fec.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f0514c4015765d1b12b76f4df81215.png)
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7 . 证明:
(1)若
,求证:
;
(2)若
,求证:
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae41b4ea7f44a8699f108def4a22ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c79de030dea51c5e80e233b44788de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d2957f2fb09a6caf84dc5a0a8dfead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5673a0c44c18320db28445ac653a0acc.png)
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8 . 已知
,
为正数,证明下列不等式成立:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa23408bcc9f6200f22a310e5f2569a.png)
(2)
(其中
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa23408bcc9f6200f22a310e5f2569a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa2b7ea83c42b08f7fa98f40b7ceb797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
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9 . (1)已知
,且
,求证,
.
(2)若
,求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a0aa068c979c53361d049ce49987a8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353a0504082335c98b71653317beabbe.png)
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10 . 完成下列不等式的证明:
(1)对任意的正实数
,
,
,证明:
;
(2)设
,
,
为正实数,且
,证明:
.
(1)对任意的正实数
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eefb6ab060d0a77a4e5f5659315000d.png)
(2)设
![](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/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3271651d8894a4b7413b402f9723975.png)
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