解题方法
1 . 证明下列不等式:
(1)已知
,求证:
;
(2)已知
,求证:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9656db3a38e6c58dc5ceb291173053a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829e09e0f8adbcb6ca7e8902019729f6.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc2bb608dcbe043ded3b74d4a8b5140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d2a05075997525049a368aba1c2b46.png)
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解题方法
2 . (1)
,
,其中x,y均为正实数,比较a,b的大小;
(2)证明:已知
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af972332e5a9149d66e5a2577e71d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2b8f0b94dcf960ca3659536d077d62.png)
(2)证明:已知
![](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)
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2022-05-05更新
|
1061次组卷
|
8卷引用:河南省濮阳市油田第二高级中学2021-2022学年高二上学期9月考试文科数学试题
河南省濮阳市油田第二高级中学2021-2022学年高二上学期9月考试文科数学试题广东省广州市铁一三校2022-2023学年高一上学期期中数学试题贵州省兴义市顶效开发区顶兴学校2022-2023学年高一上学期期中考试数学试题内蒙古包头钢铁公司第四中学2022-2023学年高一上学期期中考试数学试题(已下线)3.1 不等式的基本性质 (1)(已下线)专题2.2 等式性质与不等式性质-重难点题型检测-2022-2023学年高一数学举一反三系列(人教A版2019必修第一册)2.1 等式性质与不等式性质练习河南省周口市鹿邑县第二高级中学校2023-2024学年高一上学期第一次月考数学试题
解题方法
3 . 证明:
(1)已知a>b>0,c<d<0,e<0,求证:
;
(2)已知x>0,y>0,x+y=1,求证:
.
(1)已知a>b>0,c<d<0,e<0,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d2a05075997525049a368aba1c2b46.png)
(2)已知x>0,y>0,x+y=1,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0050f60381c11bd08745623096f0a66e.png)
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4 . (1)设
,证明:
.
(2)已知正实数
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ada798eeba5bd19d497bfd0741afd00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6320fbdc13c4ab88cf8f577cce4001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e14cc5eb8fc0c17058e33ae8e3765f.png)
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5 . (1)已知
,且
证明![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
(2)已知
是正实数,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a93645a9c1f5a2961519d74bf51567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e906ec0f947d031f8f426272176e7753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d701d16d9f318ee8fa779f5b961d64c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3095b59b062a298fb3c4a9c45f57d9.png)
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2020-10-23更新
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212次组卷
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2卷引用:江苏省扬州市公道中学2020-2021学年高二上学期期中复习数学试题
解题方法
6 . 证明:(1)已知a,b,
,
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
(2)已知a,b,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede693e9fed26c40f6fee9c3aaad147c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
(2)已知a,b,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede693e9fed26c40f6fee9c3aaad147c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f917a19a15bceb9a3769e59e25dd9c.png)
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2020-09-01更新
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207次组卷
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2卷引用:新疆阿勒泰地区2019-2020学年高二下学期期末考试数学试题(A卷)
名校
解题方法
7 . 已知
,若m,
,求证:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736085d5dadfb7081c13acb12899490a.png)
(2)设a,b是两个不相等的正数,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdcfc71b422a73d7110b17e57c0e161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9b6ad6f6fce0c84edfbc7b9802e3d7.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736085d5dadfb7081c13acb12899490a.png)
(2)设a,b是两个不相等的正数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f00f997ae12c30f551adb834e1d7ef8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5d2a320b9ff137ce3632296c4b1d79a.png)
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8 . 分析法又叫执果索因法,若使用分析法证明:“已知a>b>0,求证:
-
<
.”最终的索因应是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d012d124f04963fb72a68af40d5f8f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c462d08d75fcc7ccf9c3ecea1972e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c632c082ad3e3fd8389b26d0875559.png)
A.![]() | B.![]() | C.1<![]() | D.a-b>0 |
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2019-05-19更新
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241次组卷
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2卷引用:吉林省蛟河市第一中学校2018-2019高二下学期期中考试数学(理)试题
9 . 求证:
.
证明:因为
和
都是正数,
所以为了证明
,
只需证明
,
展开得
,即
,显然成立,
所以不等式
.上述证明过程应用了( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1982787c165f45dc0af0c166da31c7b4.png)
证明:因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650ef902d427468119ea4f00fc2717ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
所以为了证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1982787c165f45dc0af0c166da31c7b4.png)
只需证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe58bdfab519bbc0ba1c1290741da65e.png)
展开得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d7b886ac3f3507463c7313f681b7a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa71cf12282f0c34a439b7b66c121006.png)
所以不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1982787c165f45dc0af0c166da31c7b4.png)
A.综合法 |
B.分析法 |
C.综合法、分析法混合 |
D.间接证法 |
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2024高一上·全国·专题练习
解题方法
10 . 设a,b,c均为正数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2078d18b96d1d777dc353beedf90e5e.png)
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