名校
1 . 设
,
,
都是正数,且
.
(1)求
的最小值;
(2)证明:
.
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f6a1730b69e56db541821513a1bbbb.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3feaa7c319b102fd429dccde352c7e7b.png)
您最近一年使用:0次
2020-05-13更新
|
1205次组卷
|
5卷引用:江西省萍乡市芦溪中学2022-2023学年高二(尖子班)上学期开学考试数学试题
名校
解题方法
2 . (1)已知
、
、
、
是正实数,求证:
,当且仅当
时等号成立;
(2)求
的最小值,并指出取最小值时
的值.
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29574517e0bd98aa055ee15120f8fff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbd4e25575245b5688f4b6e395fcd1c.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef9fd14d59c0e078198c430fb6e8bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
名校
3 . 如果
,且
,那么
,证明过程如下:证明:构造函数
,则
,因为对一切
,恒有
,所以
,从而得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55315c5c313adb7180217928afc264c9.png)
用与上述不同的方法证明命题
;
若
,且
,请写出命题
的推广结论.(无需证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8400360babef946f0a248331e84fc841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e5dadfc7d9b12bea102cc0ce5bfcc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55315c5c313adb7180217928afc264c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3fb85bbc662da6038cd0c21425a2e5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d124f54625949773c8efb99278c955be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf1a735cc2c937ba13a20234c3efa146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55315c5c313adb7180217928afc264c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a70a389616c5ad7341083a8f1f25ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1372214137819172b4a42c54a51dd90d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次