1 . 伟大的数学家高斯说过:几何学唯美的直观能够帮助我们了解大自然界的基本问题
一位同学受到启发,借助上面两个相同的矩形图形,按以下步骤给出了不等式:
的一种“图形证明”.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/8/baab102d-4642-4d80-ac4e-405b1c9d2e7d.png?resizew=298)
证明思路:
(1)图1中白色区域面积等于右图中白色区域面积;
(2)图1中阴影区域的面积为
,图2中,设
,图2阴影区域的面积可表示为______
用含
,
,
,
,
的式子表示
;
(3)由图中阴影面积相等,即可导出不等式
当且仅当
,
,
,
满足条件______ 时,等号成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0bbac8f3e00fd58c206d93a20a3f92.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/8/baab102d-4642-4d80-ac4e-405b1c9d2e7d.png?resizew=298)
证明思路:
(1)图1中白色区域面积等于右图中白色区域面积;
(2)图1中阴影区域的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27562a5708b98d015cf417e65dc8e5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb689a793465929f004e561242fa993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(3)由图中阴影面积相等,即可导出不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8f5cb1ec1f91de107169495a47cbba.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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
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2018-01-22更新
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2卷引用:北京市朝阳区2018届高三第一学期期末理科数学试题