1 . 解不等式组及计算:
(1)解不等式组![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b2fdadaaec3762b29658146dd94010.png)
(2)因式分解:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93aeb4732bc25e7793e70e618e2a60b5.png)
(3)解方程:
;
(4)先化简,再求值:
,从
,0,2中取一个合适的数作为x的值代入求值.
(1)解不等式组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b2fdadaaec3762b29658146dd94010.png)
(2)因式分解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93aeb4732bc25e7793e70e618e2a60b5.png)
(3)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4a16ba60d105e018f5bad9ed3e3ad0.png)
(4)先化简,再求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0053981d6fa80df1c15ec84fccd700a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
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2 . 回答下列各题:
(1)计算:
.
(2)求不等式组
的解.
(3)先化简,再求值
,其中x的值是方程
的根.
(1)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d37748a847ea07f86e9d8987fc41b0.png)
(2)求不等式组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e43d080c3647643a56a853d0e4685d6.png)
(3)先化简,再求值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668ff378ae340df95a355acaf5806bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8034dddd265a186e29172623e3b9eadf.png)
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3 . (1)求不等式组
的整数解,可按下列步骤完成解答:
①解不等式①,得:
②解不等式②,得:
③把不等式①和②的解集在数轴上表示出来:
④原不等式组的解为:
⑤原不等式组的整数解为:
(2)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410029de91aa64a49d81f35df1489d17.png)
①解不等式①,得:
②解不等式②,得:
③把不等式①和②的解集在数轴上表示出来:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/3/5abc164c-86c8-44db-8c59-1bdb001a0ffe.png?resizew=232)
④原不等式组的解为:
⑤原不等式组的整数解为:
(2)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/488c8a8ed3c5ccbf289849967ad572d8.png)
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4 . (1)解不等式组:
,并把解集在数轴上表示出来;
(2)先化简,再求值:已知
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e4348a5183fcf3686773969d85c3921.png)
(2)先化简,再求值:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc12fed7a6f4777c0fccc896e624281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde4df5d30068f1efab9f40c2f24b623.png)
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名校
5 . 解方程或不等式
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c3a62a60d6980ce31614850fdeb0f4.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39832874059a4eba9897f2f1e741fa7.png)
(3)求不等式组
的最大整数解.
(4)解关于
的分式方程
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c3a62a60d6980ce31614850fdeb0f4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39832874059a4eba9897f2f1e741fa7.png)
(3)求不等式组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea34731ab35d0b4a20ece917d4095028.png)
(4)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3ae53c2c99b654c95e87623fc75eab4.png)
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名校
6 . (1)解不等式组:
(2)先化简,再求值:(
-
)÷
,其中x=
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731bc155992954c7899fb0669576e594.png)
(2)先化简,再求值:(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60b122e651b49f676e07bd8c815006f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76241e782e13eeee7c187507778aecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b05e238548dc202137a63d8b20ff277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
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7 . 已知反比例函数
的图像经过点
.
(1)求
的值为 ;
(2)完成下列解答:解不等式组![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504df4bcf895161e82a657da3c5e082a.png)
(Ⅰ)解不等式①,得 ;
(Ⅱ)根据函数
的图像,得等式②的解集为 ;
(Ⅲ)把不等式①和②的解集在数轴上表示出来,得到不等式组的解集为 ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7e80d8fb6c014b585cb0902275600b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)完成下列解答:解不等式组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504df4bcf895161e82a657da3c5e082a.png)
(Ⅰ)解不等式①,得 ;
(Ⅱ)根据函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
(Ⅲ)把不等式①和②的解集在数轴上表示出来,得到不等式组的解集为 ;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/f840ee68-a215-486b-b43f-a1e1152c8e5b.png?resizew=218)
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8 . (1)对实系数的一元二次方程可以用求根公式求复数范围内的解,在复数范围解方程
;
(2)对一般的实系数一元三次方程
(
),由于总可以通过代换
消去其二次项,就可以变为方程
.在一些数学工具书中,我们可以找到方程
的求根公式,这一公式被称为卡尔丹公式,它是以16世纪意大利数学家卡尔丹(J. Cardan)的名字命名的.卡尔丹公式的获得过程如下:三次方程
可以变形为
,把未知数
写成两数之和
,再把等式
的右边展开,就得到
,即
.将上式与
相对照,得到
,把此方程组中的第一个方程两边同时作三次方,
,并把
与
看成未知数,解得
于是,方程
一个根可以写成
.
阅读以上材料,求解方程
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed344791b8b035ca04d4b5af7364cae5.png)
(2)对一般的实系数一元三次方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ad9d68d15b5d5121fcf99ebddaa986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0f3c81f415857813838d4b9b714d56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea05ab19c339e26f8268fbc7b6e918d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5dd275a6062b21f9c3e9155c7e0ba62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5dd275a6062b21f9c3e9155c7e0ba62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ead1b77b69e6b51d6d483331fd01d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0bed1a02239821a616bc173181e7ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c26aacdd3362aa65b2966045cbfcddf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f02c3aa1326c9b1e069b6997cd29bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11792ad247341c0dbc80663dd0fa6f77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ead1b77b69e6b51d6d483331fd01d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1e8aa11c220ffef18a553784e1ecc16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491db400b0e81be11e3fd8729fe61a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36accab23dbd172687769aea43e5781c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411a315870ed3e6d0e8ea885f1a04bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9930c09269f4f03794e38c17f6da67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5dd275a6062b21f9c3e9155c7e0ba62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d63387694fd1caafce80adfb43c86b.png)
阅读以上材料,求解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93c3d494147195cf4f5e1fa3f6f5a0b9.png)
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9 . (1)解方程:
;
(2)解方程
;
(3)解方程组
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bedf894f1ce8ccdb64ddb3a86feb7b46.png)
(2)解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0f2225c51f88aa9fc4f783525fb0c2.png)
(3)解方程组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b402a08175027f5f4811f60ff4adeb5.png)
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解题方法
10 . (1)化简求值:
;
(2)解关于x的不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5796a837ce061d7494540f0bc522923f.png)
(2)解关于x的不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7232718d2d78bad722a2ffc476059bc0.png)
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