名校
1 . 请同学们补全下面两个关于x的不等式的解答过程.
(1)
;
解:令
,
令
,计算
,
当
时,即
时,方程
不存在实根;
画
草图,
不等式的解集为______.
当
时,即______时,方程
的两根为______.
画
草图,
不等式的解集为______.
当
时,即______时,方程
的两根为______.
画
草图,
不等式的解集为______.
(2)
.
解:令
(*),
则方程(*)的三个根从小到大排列分别为
______;
______;
______.
把三个根分别标在x轴上,并完成表格,
请根据表格写出不等式
的解集.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/458cbcd84273373e0a0bdab32ad42bad.png)
解:令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4317c59a6012372bc027d7badec24f.png)
令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06295591972865ce5a2fafb1427aa707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c70eef4e278303db019587ee2cc20f.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc39e3f9688bc77675ffdf0dd79da142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6232dc74b15e4acb0ac3482a1cbe6a52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06295591972865ce5a2fafb1427aa707.png)
画
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925d9d720033e5e20561eb5f0722ecef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/6/b7500d30-d563-4620-8611-50152041ac5f.png?resizew=165)
不等式的解集为______.
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2b0eb6b8e515c616b5cdd4c37fefc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06295591972865ce5a2fafb1427aa707.png)
画
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925d9d720033e5e20561eb5f0722ecef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/6/f7cb6ca2-bf56-448e-896a-91b0659d6ed3.png?resizew=164)
不等式的解集为______.
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda1e6337ff7355c2fe9c19f9d619f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06295591972865ce5a2fafb1427aa707.png)
画
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925d9d720033e5e20561eb5f0722ecef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/6/3bdfb626-c867-473d-bcff-8423f5c61714.png?resizew=166)
不等式的解集为______.
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef1d654789c54f96acda1437cffb865.png)
解:令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8fa5322900d260782795939a4085c3.png)
则方程(*)的三个根从小到大排列分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e92f14fb20f920f88dcad2ccd1d53f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dad5a12f34bed0da0de93beae0eaa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7ad31dd3397f7d2830182a8d309289.png)
把三个根分别标在x轴上,并完成表格,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/6/9af896b0-08b8-4ac2-980e-9da2035e8cbd.png?resizew=271)
x的取值范围 | ||||
|
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef1d654789c54f96acda1437cffb865.png)
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