1 . 不等式的基本性质:(1)传递性:__________ .
(2)可加性:___________ .
(3)可积性:①___________ ;②___________ .
(4)同向可加性:___________ ;异向可减性:___________ .
(5)同向正数可乘性___________ ;异向异号可乘性:___________ ;异向正数可除性:___________ .
(6)乘方法则:___________ (
,
).
(7)开方法则:___________ (
,
).
(8)倒数法则:___________ ;___________ .
(2)可加性:
(3)可积性:①
(4)同向可加性:
(5)同向正数可乘性
(6)乘方法则:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(7)开方法则:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(8)倒数法则:
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2023高一·全国·专题练习
2 . 基本不等式求最值
(1)设x,y为正数,若积xy等于定值P,那么当x=y时,和x+y有最小值_____ (简记为:积定和最小).
(2)设x,y为正数,若和x+y等于定值S,那么当x=y时,积xy有最大值
S2(简记为:和定积最大).
(1)设x,y为正数,若积xy等于定值P,那么当x=y时,和x+y有最小值
(2)设x,y为正数,若和x+y等于定值S,那么当x=y时,积xy有最大值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
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20-21高一上·全国·课前预习
3 . 绝对值不等式:______ .
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20-21高一上·全国·课前预习
4 . 数轴上的中点坐标公式:一般地,如果实数a,b在数轴上对应的点分别为A,B,即A(a),B(b),如果线段AB的中点M对应的数为x,则x=____ .
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5 . 含有绝对值的不等式基本性质
(1)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92937c151ba93bda54239e4e86c2ce0.png)
___________ ;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba713ae0552b1aa38c88505580301380.png)
____________ ;
(3)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92937c151ba93bda54239e4e86c2ce0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba713ae0552b1aa38c88505580301380.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7afdcf504701c8dd37706106686dcc08.png)
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6 . 不等式的性质
(1)
;
(2)
;
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198d6164caabb29245ec761166a1cfa1.png)
推论1
;
推论2
.
(4)
①____________
;
②__________
.
推论1
;
推论2
;
推论3
.
(5)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68bab8531ef17ff18c12de3f437b52a1.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/886ecbcd1be433b38f55198420b28615.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198d6164caabb29245ec761166a1cfa1.png)
推论1
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20787315e55a437eb4f2c7a1cf3c11b0.png)
推论2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ccb75bf390487671e2241bfeb13b71.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75ce26e1400660921a4e059819c78924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52248b06a0349c0d938bac6ebfc8abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75ce26e1400660921a4e059819c78924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a6d32ec78ea2ab27f7f64cd77a5c2b.png)
推论1
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a3e09b40351f8b6cf0bf303100a151.png)
推论2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329a68b064574c1a8974d47996903d53.png)
推论3
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08007ace9b71e66887c47a92f7de365f.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65bc07912a9b5b4434489724e10590f.png)
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7 . 比较两个实数大小
两个实数的大小是用实数的运算性质来定义的,有:
__________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8eeaf3726cb66fdcf397325503b8bb.png)
__________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0496a699802e3d531b7f25687bb5e2.png)
____________
另外,若
,则有
;
;
.
两个实数的大小是用实数的运算性质来定义的,有:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96753485da057c182d05d56917b55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8eeaf3726cb66fdcf397325503b8bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0496a699802e3d531b7f25687bb5e2.png)
另外,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25747252e57c76fc56f60be6eecfada9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71599f6749e42bdc3c09cfd5002c0fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6c2cbac488e50397e23b703a78d144.png)
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2022-08-23更新
|
943次组卷
|
2卷引用:章节整体概况-一元二次函数、方程和不等式