1 . 解下列关于
的不等式或不等式组:
(1)设
,解不等式:
;
(2)解不等式组:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc05cde4f00587cf3e7d3524b2bddf4.png)
(2)解不等式组:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7794539786aff30ed0e24158db88ae6b.png)
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名校
2 . (1)解方程组
;
(2)解关于
的不等式
;
(3)已知关于
的不等式
的解集为
,求关于
的不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9875224051c04670bea42c9a25304076.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3aee08ad8c82acbf3b6a1c3824f2383.png)
(3)已知关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5f28031b036e4a37be931d5ff28368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009db35e84f9e2ed847519211918fbfe.png)
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2023-11-05更新
|
84次组卷
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2卷引用:北京市十一学校2023-2024学年高一上学期教与学质量诊断(期中)考试数学试题
3 . 解下列各题:
(1)解不等式:
;
(2)计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03356b51d55a5d49d6fa710ecc885f4c.png)
(3)设
是非零实数,已知
的值.
(1)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db7dc6d6d563e64470ad7c0196b75a3.png)
(2)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03356b51d55a5d49d6fa710ecc885f4c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7f321c2a74ef6e75ff3a4252323457.png)
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解题方法
4 . 关于
有不等式 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdf5cd927023a2bdcdd3d6f70e71d7f3.png)
(1)当
时, 解不等式.
(2)若不等式仅有一解,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdf5cd927023a2bdcdd3d6f70e71d7f3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff4b08995815b1bcba83e12a9aec4fb.png)
(2)若不等式仅有一解,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca35310a128febf44f147d4df340d57a.png)
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2023-11-08更新
|
161次组卷
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2卷引用:浙江省温州十校联合体2023-2024学年高一上学期期中联考数学试题
2024·全国·模拟预测
解题方法
5 . 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)
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2022高一·全国·专题练习
名校
6 . 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
|
1556次组卷
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6卷引用:专题5 三个二次的关系(基础版)
7 . 关于x的不等式
.
(1)若不等式的解集为
,求
的值,并解关于x的不等式
的解集.
(2)若
,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae8fff7c98b78992edcd61daf6ea72f.png)
(1)若不等式的解集为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae96c0396bbf254f04e77615eac5fd4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6368286b2b9275c4d1831384361db1d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db01c0b80e146432c30073258884736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae8fff7c98b78992edcd61daf6ea72f.png)
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8 . 定义区间
、
,
、
的长度均为
,其中
.若不等式组
的解集中各区间长度和等于8,则实数t的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd4d438ae7d4da0e100bb92d622c866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a381cebfeee07ae150cdeff6e7a64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eae51f0310b87cde2e206643e9d25a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f03d4f1c1607a15b59cc39eb866548.png)
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解题方法
9 . 已知集合
.
(1)当
时,关于
的不等式组
没有实数解,求实数
的取值范围;
(2)若
,且关于
的不等式
的解集为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d57c293ebc3b99cb7aff9b3e585dcdc7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bc9551406faf1c4f1e444dbd66237b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2454a6dc18fdf2cde16cb1b096ea8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811625bead5bd88970550be98125aa3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5258a748e0915550223745b9d4aa68f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
10 . (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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2024-05-19更新
|
811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