解题方法
1 . 证明以下结论:
(1)已知
,求证:
;
(2)若
均为实数且
.求证:
中至少有一个大于0.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ada798eeba5bd19d497bfd0741afd00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbc2278547879e9246de7e749a774d7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ebe6c33debb66a7cbc9ecddc6c89de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
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2 . (1)求证:
;
(2)已知函数
,用反证法证明方程
没有负数根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04fdf048f747aa8a3790f0100aa1f92.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a6bdcb5a8eaa7b0c2c0dcae47899b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
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2018-06-15更新
|
478次组卷
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2卷引用:【全国市级联考】江西省泰和县二中、吉安县三中、安福县二中2017-2018学年高二下学期三校联考数学(理)试题
3 . 用适当的方法证明下列命题:
(1)
;
(2)设
,求证:三个数中
,
,
至少有一个不小于2.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45597a8f1782f1cdd29b06650b7a5fdf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af36a3b0f5f36d3e70d5af4b2de6bd44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2582892eba557b99dbe879efb9754d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7b2877e9e163191cdca767a7ecbb3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f369f9464a202b71aa11872c8e6a1543.png)
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4 . (1)当
时,试用分析法证明:
;
(2)已知
,
.求证:
中至少有一个不小于0.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6c5526947e9bef051bc3bdf7fd186d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b1411bbc505b5056e68e077d18e06b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003fe3cdffd8338cf5766dd287b0c5e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
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2017-05-03更新
|
834次组卷
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5卷引用:江西省贵溪市实验中学2020-2021学年高二3月第一次月考数学(文)试题
5 . (1)已知
,求证:
.
(2)已知
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed105ddc16a6a83ff5126fdc773b3488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e3bbf56c264002fe8afc45a864f5bd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360ff131c51a4ef6745538c18cec92c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4017ae27c7e8d9a278cdae696bd93c88.png)
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6 . (1)已知x>0,y>0,
,求证:
.
(2)a,b,
,求证:
,
,
不能都大于1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128294be1f10b83df30ad60d4c696224.png)
(2)a,b,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c415b871cbdc3215c1eacf1ed11dae6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d15cd3a09a5b2b7caebab7dd96852533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8d46fedbb81f3db10b826257b88912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e78bb8432a969c5d89bdd628501fd56.png)
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2022-06-02更新
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249次组卷
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3卷引用:江西省吉安市安福二中、井大附中、吉安县三中、遂川二中2021-2022学年高二下学期四校联考(第三次月考)数学(文)试题
7 . 求证:
(1)已知
,求证:
;
(2)已知a>0,b>0,且
,求证:
与
不可能同时成立.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae41b4ea7f44a8699f108def4a22ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f4fa6828188864939832ab3c23197a.png)
(2)已知a>0,b>0,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7dec5f5ef4a53175966c1704ad8a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656cacf9b32ce8f718dcb50bc8994593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f678dde8a2f44b8eae985b11bf4b50.png)
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2022-05-02更新
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2卷引用:江西省景德镇一中2021-2022学年高二下学期期中考试数学(文)试题
名校
8 . 已知函数
.
(1)用反证法证明方程
没有负根.
(2)证明:过点
有且仅有两条直线与曲线
相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bec331655a9cb42e298431759588ede6.png)
(1)用反证法证明方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
(2)证明:过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0d32ea3bbad35e0af9ecff1c62d044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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2022-03-20更新
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7卷引用:江西省赣州市于都县第二中学等六校2021-2022学年高二下学期期中数学(理)试题
9 . (1)设
,
,
,用反证法求证:下列三个关于
的方程
,
,
中至少有一个有实数根.
(2)已知
,且
,用分析法求证:
.
![](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/d1142d98adcce0ebb57fd0f7dde47ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f11b42957b6d2b70a59d32754829ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fc3dfb3c04b3acedcb350e4cc6f508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e845cbc83f334e9b0be6961ae2c875.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d100c22435a23e017cfe6f535379d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30875e7cfac45255f530695e08950be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b3ec736096bdc7523763da1ecc1cc3.png)
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10 . (1)用反证法证明:在一个三角形中,至少有一个内角大于或等于
.![](https://img.xkw.com/dksih/QBM/2021/5/17/2722889158672384/2786853519319040/STEM/32f21502ef5d4f61a5af6378dd696657.png?resizew=24)
(2)用分析法证明:对于任意
,
,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://img.xkw.com/dksih/QBM/2021/5/17/2722889158672384/2786853519319040/STEM/32f21502ef5d4f61a5af6378dd696657.png?resizew=24)
(2)用分析法证明:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11438650a06e47cdfab97d4d5f4b88f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e8010392b125fb5f015992bad5d6fa.png)
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