名校
解题方法
1 . 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
|
98次组卷
|
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
2 . (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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解题方法
3 . 选用恰当的方法证明下列不等式
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679e658fa5679ce73e1b5fdfe434b724.png)
(2)已知
,证明:
.
(3)已知a,b,c均为正实数,求证:若
,则
.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679e658fa5679ce73e1b5fdfe434b724.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa4f85f4d4f4bd9edaa8a964565ca1a.png)
(3)已知a,b,c均为正实数,求证:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a57e060f61f7efa54982bda67db483a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d54c9eb01acfe09c34cb808326cc5e.png)
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4 . 若函数
对任意的
均有
,则称函数具有性质
.
(1)判断下面函数①
;②
是否具有性质
,并说明理由;
(2)全集为
,函数
,试判断并证明函数
是否具有性质
;
(3)若函数
具有性质
,且
,求证:是否对任意
,
均有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6f347571b113ba7618c56958ea233f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断下面函数①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbe323771bc92bf5767e1bd9a46b946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c904567c3b3734e1eca8d042ef7a7b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)全集为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2029fc48d77259461f693025c39924be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390b9e64771945e2a8119dfebd8cfdea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d1a406338067cfdeafaf575b2fbcdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff2aa68223dfc02f39d7d10fa005387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92d934e15c3727e7f56e3907237c736f.png)
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2021-11-23更新
|
864次组卷
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2卷引用:辽宁省沈阳市五校协作体2021-2022学年高一上学期期末联考数学试题
名校
5 . (1)若
且
,求证:
;
(2)若
为正实数,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481ee0d1e39e92a4732eea90225eb94c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce37be14cad3e2409eada581dc029aca.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7dbc702617c765a573961953cc0901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16195724ab65f5ed0f378a14051ff5bd.png)
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6 . 选用恰当的证明方法,证明下列不等式.
(1)证明:求证
;
(2)设
,
,
都是正数,求证:
.
(1)证明:求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c19d94ff48082c1cd213c82c99abf0.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/533937a08d1ed87594ac52c658be9649.png)
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2019-11-23更新
|
1312次组卷
|
3卷引用:辽宁省大连市2019-2020学年高一上学期期中数学试题
辽宁省大连市2019-2020学年高一上学期期中数学试题安徽省池州市青阳县第一中学2020-2021学年高二下学期3月月考文科数学试题(已下线)2.2基本不等式-2021-2022学年高一数学同步辅导讲义与检测(人教A版2019必修第一册)
10-11高二下·内蒙古赤峰·阶段练习
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7 . 已知三角形ABC的三边长为a、b、c,且其中任意两边长均不相等.若
成等差数列.(1)比较
与
的大小,并证明你的结论;(2)求证B不可能是钝角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f81b8a02e231884bc36fdc4870830cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61fe34b1cc3a3cfcfad66fb03b9e22c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c147d6cbd7cbaeb8ec08a0ba69cd59dd.png)
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2016-12-01更新
|
827次组卷
|
8卷引用:辽宁省铁岭市六校协作体2022-2023学年高三质量检测数学试题
辽宁省铁岭市六校协作体2022-2023学年高三质量检测数学试题(已下线)2010-2011年内蒙古赤峰市田家炳中学高二下学期4月月考考试数学文卷(已下线)2011-2012学年河南省周口市高二下学期四校第一次联考文科数学试卷河南南阳一中2015-2016学年高二下第二次月考文科数学试题内蒙古巴彦淖尔市杭锦后旗奋斗中学2017-2018学年高二下学期第一次月考数学(文)试题2018-2019学年人教版高中数学选修1-2 模块综合评价(一)黑龙江省海林市朝鲜族中学人教版高中数学选修1-2同步练习:模块终结测评(二)河南省郑州市巩义中学2019-2020学年高二下学期期中考试数学(文)试题
名校
解题方法
8 . 基本不等式可以推广到一般的情形:对于
个正数
,它们的算术平均不小于它们的几何平均,即
,当且仅当
时,等号成立.若无穷正项数列
同时满足下列两个性质:①
;②
为单调数列,则称数列
具有性质
.
(1)若
,求数列
的最小项;
(2)若
,记
,判断数列
是否具有性质
,并说明理由;
(3)若
,求证:数列
具有性质
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efff8ec14cb242e793afab4468bf2e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2617515e5ce81b3f5d9f4e806b21b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6879960be91ea52297d587e9a014f54a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce59ae5baacab766b0915722377a746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bc99b9545c8c838e99b7be9c6d1046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f20e03ee7d9307a0a4d242fffda381d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d013861990cf331c82eb453416ae31bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4247739746b8ddf1403541047e8b5580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2024-02-21更新
|
3162次组卷
|
7卷引用:辽宁省朝阳市建平县实验中学2024届高三第五次模拟考试数学试题
辽宁省朝阳市建平县实验中学2024届高三第五次模拟考试数学试题安徽省部分省示范高中2024届高三开学联考数学试卷湖南省2024年高三数学新改革提高训练三(九省联考题型)湖北省荆州市沙市中学2024届高三下学期3月月考数学试题(已下线)黄金卷04(2024新题型)广东省广州市西关外国语学校2023-2024学年高二下学期期中数学试题(已下线)压轴题03不等式压轴题13题型汇总-2
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9 . 平均值不等式是最基本的重要不等式之一,在不等式理论研究和证明中占有重要的位置,基本不等式
就是最简单的平均值不等式.一般地,假设
为n个非负实数,它们的算术平均值记为
(注:
),几何平均值记为
亦(注:
),算术平均值与几何平均值之间有如下的关系:
,即
,当且仅当
时等号成立,上述不等式称为平均值不等式,或简称为均值不等式.
(1)已知
,求
的最小值;
(2)已知正项数列
,前n项和为
.
(i)当
时,求证:
;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb90c316d8a99694396de80ed0b0cf25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2b043b989216035c6fd985f1dd6a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62039675c3c14eb40435c837baac504b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/616f78142aa5d339a92737356cb5f034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3381745623cb1a441da9c0d591eb5fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cdd81b8b615961adae7ec165aacfad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434d0c6ca47b1b7af2f3ff0b7663d908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c294bd0c22262b46c1ba57f8f1dc8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01cc4e11e7cd0174262dfe66662a6a33.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d229cbec798c9c278a9b5979cb38247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59149e37a56078d30e6e734fde3d6f5f.png)
(2)已知正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d72bba8881efc02361163a97c6dde32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9021d923afeecdbb8c55e283c26704a.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237e3090bb2c02d7b62fa5d3d41b63b5.png)
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10 . 如图,正方形
中,
分别为线段
上的点,满足
,连接
交于点
.
;
(2)设
,求
的最大值和
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3355e2fa0ac6c675f02ee36c3ced4f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f8eebda19eded2b059774a8c2666c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9bfb96c6a7b5bf01bb15042355ac215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f49d1de7c6dfc04b6e84e23eec0a1d7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8979e5728aef6fa57b6970525afcb6c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a61103ea69687ba91d5b380c0e2238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d6a99033826bd1b44f58b9e11ff52e.png)
您最近一年使用:0次
2024-04-11更新
|
408次组卷
|
2卷引用:辽宁省抚顺市第一中学2023-2024学年高一下学期3月月考数学试题