1 . 已知函数
有两个零点
,则可设
,由
,所以
,
,这就是一元二次方程根与系数的关系,也称韦达定理,设多项式函数
,根据代数基本定理可知方程
有
个根
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331d5e308cd5469e0f28a8d75f79903f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e38a748661547c23dc5bb7727157a272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cce519ecad53af16de6b8fa9434110e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05dd02b6f561dcf94bab8a3160108d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897630dd340ec6c6b20cdd754d0a12c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bdb2ad96ef43cf5e427d7a2d9fafe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83590c4a7ea5636843dd4b60c67cb40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0a7f3b30ea5e3955d435792fa71698.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 我国古代数学名著《九章算术》的论割圆术中有:“割之弥细,所失弥少,割之又割,以至于不可割,则与圆周合体而无所失矣”,它体现了一种无限与有限的转化过程.比如在
表达式中“…”既代表无限次重复,但原式却又是个定值,它可以通过方程
解得
,类比上述方法,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438b23e66b71f04eddca39a8d8e2164b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6977b6bb77c43822da13161ab1e674bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e3a9c7590825bfeeff83359c2513346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe1b2e138a08bafc722260eeaab03e9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-05-05更新
|
1366次组卷
|
3卷引用:四川省内江市2022届高三第三次模拟考试数学(文)试题
3 . 已知一元三次方程
的三个根分别为
、
、
,请类比一元二次方程的韦达定理的证明,给出一元三次方程的根与系数的关系并且给出相应证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eccb3856fa5aa8dc822a593ec88ca2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
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20-21高一·江苏·课后作业
4 . 子集符号“
”与不等号“
”看起来很相似.“
”具有下面的性质:
如果
且
,那么
;
如果
且
,那么
.
试写出“
”相应的“性质”,并判断其正确性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b980d8446f130dfc405c196109e73ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8536a5ebd76f494c03019086506d8e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8536a5ebd76f494c03019086506d8e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3798d6c2e5eac9c1d8b044efd5081acf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed71b5f6cf02b7e4c52c1181669a3879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698cb6e11f584b58e6b0eb0753c79258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3798d6c2e5eac9c1d8b044efd5081acf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c659396f6a0f72e213185b1ab2e198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
试写出“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b980d8446f130dfc405c196109e73ea4.png)
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5 . 下面给出的类比推理中,结论正确的是( )
A.由“![]() ![]() |
B.由“![]() ![]() |
C.由“边长为![]() ![]() ![]() ![]() |
D.由“若三角形的周长为![]() ![]() ![]() ![]() ![]() ![]() |
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6 . 若一个带分数的算术平方根等于带分数的整数部分乘以分数部分的算术平方根,则称该带分数为“穿墙数”,例如
.若一个“穿墙数”的整数部分等于
,则分数部分等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d1831c3d328c26359561e1837039fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7db82a3e9a06d55b5e90d0aade9c64.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 我们曾用组合模型发现了组合恒等式
,这里所使用的方法,实际上是将一个量用两种方法分别算一次,由结果相同来得到等式,这是一种非常有用的思想方法,叫做“算两次”,对此,我们并不陌生,例如列方程时就要从不同的侧面列出表示同一个量的代数式.
(1)某医院有内科医生8名,外科医生
(
)名,现要派3名医生参加赈灾医疗队,已知某内科医生必须参加的选法有66种,求
的值;
(2)化简:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092d5cf7ee736195147eed7aedf84d76.png)
(1)某医院有内科医生8名,外科医生
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee18d7a40f7a7e0dc85b1bd75bf750c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b43f881b8c51e95cde5c5d14f00df.png)
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2021-08-24更新
|
611次组卷
|
3卷引用:江苏省南京市鼓楼区2020-2021学年高二下学期期末数学试题
8 . 我国古代数学名著《九章算术》中割圆术:“割之弥细,所失弥少,割之又割,以至于不可割,则与圆周合体而无所失矣.”其体现的是一种无限与有限的转化过程,比如在
中“…”即代表无限次重复,但原式却是个定值x,这可以通过方程
确定出来
,类似地不难得到
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7426554aa9402a66cb62d5f79dade617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52d182e17c108bb67afede31e7e83ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f1f64b6857f6239bc449eddf331a10.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021高二下·全国·专题练习
9 . 给出下面三个类比结论:
①向量
,有
类比有复数
,有
;
②实数
有
;类比有向量
,有
;
③实数
有
,则
;类比复数
,有
,则
.
其中正确的命题有( )个.
①向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b776b2381f6b85df44ef3ec351e562f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c1e7d86796fa60cfd08eaa0fbfe10a.png)
②实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d351a97edcc0783d8d7a02d041bdb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a838d9d01d18ed8cfb34d302cd74c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f965fd6d3ce968876503316dc08890bd.png)
③实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fb20e291772c2614ad19f4cc919dfec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657435e1fda84118e7f63c97505c8b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/465d1eefa80667ac537de5b68e091508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b842572e56bfa6bdec69c1695929cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6a996e043f3d89b8f90f3e55145872.png)
其中正确的命题有( )个.
A.0 | B.1 | C.2 | D.3 |
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名校
解题方法
10 . 在数学中,双曲函数是与三角函数类似的函数,最基本的双曲函数是双曲正弦函数与双曲余弦函数,其中双曲正弦:
,双曲余弦函数:
,(
是自然对数的底数).
(1)解方程:
;
(2)写出双曲正弦与两角和的正弦公式类似的展开式:
________,并证明;
(3)无穷数列
,
,
,是否存在实数
,使得
?若存在,求出
的值,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea54f9abcfb83c1f8d4860de58d9a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cea2c942a40975a4bed91960a217cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/507ea92ca0fbfa95da0f01c201ff54a4.png)
(2)写出双曲正弦与两角和的正弦公式类似的展开式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6343611e15d5f379d06115077f05d2a4.png)
(3)无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ecf3a1fecf89a37a677393d0bfe27b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7268804f4cde744cf387b933409d0c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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