解题方法
1 . 设
,
,求证下列不等式:
(1)
;
(2)
;
(3)
;
(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216682504182873f78cc43e6e46799cb.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0274fb77878866cc088d719a060e3f.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d2e0a4dc2e7a7e72c1620374e038b8.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9fc73d3810e2573cfc02488c41baab.png)
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解题方法
2 . 设
,
,比较m,n的大小关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e58293003ed8763ee5d6b7002752674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9be3ebb6f9980e57d0e8280e99bd52.png)
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3 . 判断下列命题的真假,并说明理由:
(1)若
,则
;
(2)若
,则
;
(3)若
,
,则
;
(4)若
,则
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c22b9d08cf536bbb76bce1b0f135772.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c22b9d08cf536bbb76bce1b0f135772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cbc322861846709c08c7f1da746848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f50ce6b511e6b928796e048fc7fa5c.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb54b1b3617ebc502cb44194cbcd1dc.png)
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解题方法
4 . 如图,试用直观的方法比较以
为边长的正方形的面积与四个长为
、宽为
的矩形面积之和的大小,把这种大小关系用不等式表示出来,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6f19b84484b5480ea2100165abfd81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
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解题方法
5 . 试比较下面各组中两式的大小:
(1)
与
;
(2)
与
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fcf521b88a7dbaf324df26cf67fcda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ee9408bede02c4b96a98b86e0a9766.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1bd2498d01c2d11676c0293d6de8086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc310df5a6b8fd8e1c8761ccc3bee514.png)
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2023-10-07更新
|
343次组卷
|
3卷引用:3.1 不等式的性质
6 . 某粮食收购站分两个等级收购小麦.一级小麦
元/kg,二级小麦
元/kg(
).现有一级小麦m kg,二级小麦n kg,若以两种价格的平均数收购,是否合理,为什么?
![](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/4d5556dd86322752a457b3a6ba979c80.png)
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3卷引用:3.1 不等式的性质
7 . 若
,
,判断下列不等关系是否成立,并说明理由:
(1)
;
(2)
;
(3)
;
(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cbc322861846709c08c7f1da746848.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41da25316ab8d05793f56c3c9dc168b9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522ea2b031666780e551b93fe8ca4cff.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/125415eb6733489cdc96ee48eb88aee7.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd7bbf07f7a5a7c6be88ccaaf006970.png)
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3卷引用:3.1 不等式的性质
8 . 有如图所示的两种广告牌:图(1)由两个等腰直角三角形构成,图(2)是一个矩形.试用直观的方法比较这两个广告牌面积的大小,并将这种大小关系用含字母a,b的不等式表示出来.
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3卷引用:3.1 不等式的性质
9 . 用“>”或“<”填空:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8314e2f98928b76d7fb74b09283f3db.png)
______
; (2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8314e2f98928b76d7fb74b09283f3db.png)
______
;
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad52beba3181bfc922d5c59d73a5a11a.png)
______
(
) (4)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19d2dc5a13b5ef6dbea1bd19c72ff1e1.png)
______ mb(
,
);
(5)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a60e77043cfa243c212f9e340c5f46.png)
______
(
); (6)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36accab23dbd172687769aea43e5781c.png)
______
(
).
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8314e2f98928b76d7fb74b09283f3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e26ea0261f2b67983b07b8d0bb8bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8314e2f98928b76d7fb74b09283f3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/285edfb99de8dc7317a53655aebaa39d.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad52beba3181bfc922d5c59d73a5a11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9878a063abcb6098d10560f2bf2d4b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19d2dc5a13b5ef6dbea1bd19c72ff1e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4c78214e43a8b93f2a57072033cbcf.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a60e77043cfa243c212f9e340c5f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6a2eba56d4f2d1670b0256b8d86b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66eba129d92ede31b728e2590c4db2a1.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/66eba129d92ede31b728e2590c4db2a1.png)
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3卷引用:3.1 不等式的性质
解题方法
10 . 比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af87f9699b261f7787748f9f8a2b8044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3003168e7e1a6e8131d4b049956c2a39.png)
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2023-10-02更新
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2卷引用:【导学案】3.1不等式性质课前预习-北师大版2019必修第一册第一章预备知识