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)
您最近一年使用:0次
2 . (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)
您最近一年使用:0次
2022高一·全国·专题练习
3 . 已知
,
满足方程组
,且
.
(1)试用含
的式子表示方程组的解;
(2)求实数
的取值范围;
(3)化简
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74505a91ab0c9038b2e5481131bb1342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8d93ef14e700c6bed4e4d31625925a.png)
(1)试用含
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3d52af08461102a97ea9cc12ea168a.png)
您最近一年使用:0次
2019高二上·全国·专题练习
4 . 计算:(1)解不等式:
;
(2)若关于
的不等式
的解集为
,且
,求实数
的值;
(3)解关于
的不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c447c4e739e50f3630d5ac57aa9cf0bc.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e597760cba508a4fb39c5a83f9ec2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4af0f8116d42cd991cc7a9f97e0841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe07ca2bafedb4e6145dbb01bc1af513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afeeecba13d1b662ef717fa141a46ec4.png)
您最近一年使用:0次
5 . (1)化简求值:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28d061ad25fb0a0e2918c85ffe17ad4.png)
____________ .
(2)方程
的解![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28d061ad25fb0a0e2918c85ffe17ad4.png)
(2)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28db4425b17092b429bf16bc7321b433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
您最近一年使用:0次
2022高一·全国·专题练习
6 . 已知方程组
的解满足
为非正数,
为负数.
(1)求
的取值范围.
(2)在
的取值范围内,当
为何整数时,不等式
的解为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6114d01a153cd885898f939d2fbb68bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96414f09fef9f3cc66961f371eacc285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
您最近一年使用:0次
2022高一·全国·专题练习
7 . (1)解不等式
,并将其解集在数轴上表示出来;
(2)解不等式组并把解集在数轴上表示出来:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64628175df0e4fd35d2d618e615f4bc.png)
(2)解不等式组并把解集在数轴上表示出来:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5683b7974117fff8aa416c389b985ff3.png)
您最近一年使用:0次
8 . 已知
.
(1)当
时,解不等式
;
(2)若关于x的方程
的解集中恰好有一个元素,求实数a的值;
(3)若对任意
,函数
在区间
上总有意义,且最大值与最小值的差等于2,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f782ac135ebb68ffe809837006c8f6.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b783ec4871b338c9612cbc700694e7.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e6185447373cdf38c28ba73415637c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983fa8d30993077d136d644a4de7a394.png)
您最近一年使用:0次
9 . ”鸡兔同笼”我国隋朝时期数学著作《孙子算经》中的一个有趣题目:“今有雉兔同笼,上有三十五头,下有九十四足,问雉兔各几何?”
(1)求出鸡、兔各几只?
(2)根据提示,设计这类问题的通用解法,并画出算法的程序框图.
解:设有
只鸡,
只兔,总头数为
,总脚数为
,则
,解方程得:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614338fcf6eeb0c6d36672e50518e61c.png)
用数学语言:
第一步:输入______,______;
第二步:计算鸡的只数______;
第三步:计算兔的只数______;
第四步:输出______.
(1)求出鸡、兔各几只?
(2)根据提示,设计这类问题的通用解法,并画出算法的程序框图.
解:设有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c98d21cecf0caadb3412dad3e857b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614338fcf6eeb0c6d36672e50518e61c.png)
用数学语言:
第一步:输入______,______;
第二步:计算鸡的只数______;
第三步:计算兔的只数______;
第四步:输出______.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/3c40f017-3a37-4b39-8cc9-7a804c1217af.png?resizew=83)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
10 . 在解决问题“已知正实数
满足
,求
的取值范围”时,可通过重新组合,利用基本不等式构造关于
的不等式,通过解不等式求范围.具体解答如下:
由
,得
,即
,解得
的取值范围是
.
请参考上述方法,求解以下问题:
已知正实数
满足
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb975603433961a27ff01c734d39575f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f29d5f376c75c41ae6af0c8a8565449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f29d5f376c75c41ae6af0c8a8565449.png)
由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d14a76fbd7733394b3a7a8c7508ae8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a2ebb75f6dc5ba596a98ccbc2bb9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef066cf9a851361e923ed40c97b842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f29d5f376c75c41ae6af0c8a8565449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed05aa46ec16ee8f98272565d2a2ed9.png)
请参考上述方法,求解以下问题:
已知正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb975603433961a27ff01c734d39575f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7bf9200b351a259ddfc6c0266129d.png)
您最近一年使用:0次