1 . (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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2 . 已知
.
(1)若
为奇函数,求
的值,并解方程
;
(2)解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3937b0bedd2bfe787db6c6a64bb78e21.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b35d125e80c7c1c29bf36f11c44d7c.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca28db4d93d44c5838921a45d77e320.png)
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2022高一·全国·专题练习
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3 . 已知不等式
的解为
,求
和
的值,并解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31a236a2101c170576f3c8f8e2edc1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4cf894db9fd5c3ef5af29a371416b24.png)
![](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/1c98878220e4fc94e9bfbc21a1ff2938.png)
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2022-09-05更新
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6卷引用:专题5 三个二次的关系(基础版)
4 . (1)化简求值:
;
(2)解方程:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8d8df287cf671b32274471022b6342.png)
(2)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a00a20aaf710eb93bc7c9fcc2de66fd.png)
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2022-03-29更新
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857次组卷
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3卷引用:福建省三明第一中学2021-2022学年高二下学期第一次月考数学试题
福建省三明第一中学2021-2022学年高二下学期第一次月考数学试题江苏省淮安市楚州中学、新马中学2022-2023学年高二下学期期中联考数学试题(已下线)6.2.3组合-6.2.4组合数——课堂例题
5 . (1)计算:
;
(2)解不等式组:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fb5eb938a815e834f04e92a2445af4.png)
(2)解不等式组:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9104bf8a6a8f4daeeddc5145c82375a2.png)
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解题方法
6 . (1)解不等式
;
(2)解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e35f874f2c74d693c6bfbe8ec461990.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8495da9a91bf7bfa549ca3aa4b496f37.png)
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2024-06-04更新
|
722次组卷
|
2卷引用:安徽省马鞍山市第二中学2023-2024学年高一上学期期中测试数学试卷
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7 .
,其中
是常数.
(1)假设
的解集是
,求
的值,并解不等式
.
(2)假设不等式
有解,且解区间长度不超过5个长度单位,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9529ac0c7d85536cb05f5e3f5785d5aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)假设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12578136c1a749876bb47e6f1d69988e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ff70b7bfa3d6b694958aa21f699696.png)
(2)假设不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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8 . (1)解关于
的不等式
;
(2)解不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e197de68e7d35c22dfc573c6be677cd6.png)
(2)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e88d57ca69f58353ab986ff5be88af3.png)
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2024-04-22更新
|
841次组卷
|
3卷引用:江苏省苏州青云实验中学2023-2024学年高二下学期3月月考数学试题
江苏省苏州青云实验中学2023-2024学年高二下学期3月月考数学试题浙江省金华市曙光学校2023-2024学年高二下学期4月月考数学试题(已下线)6.2.1排列-6.2.2排列数——课时作业(巩固版)
9 . (1)已知
,计算:
;
(2)解方程:
.
(3)解不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561ea6e78955142ef9dfb5550e09882f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd0a945185848a259c1d921faeae889.png)
(2)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a00a20aaf710eb93bc7c9fcc2de66fd.png)
(3)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e88d57ca69f58353ab986ff5be88af3.png)
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10 . 已知实数x,y满足方程
.
(1)求
的值;
(2)设
与
是方程组
两组不同的解,其中
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1beb6812158ca2a3082bd13ca07578f0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1afbc87ccffbc98b9ab58df8c69bee.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99307ab4373fbe72422ae5aa980db61c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41039d45e37899d233232de3d802b105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccee8eb181dc117834582bc433eca559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab3cf6695638d5bcd26580174d7cbf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da3ff6f17be99ec311610efa08ba002.png)
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