解题方法
1 . 设x、y、z均为非负实数,且满足:
,求
的最大值与最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e8bfc1fde8e1402937aee1544e766b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23f77a8e1de7f6c052b40d760f6e43d.png)
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2 . 已知
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d525f3b5704f47163c96da12dab57a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0743e74f6606dd660d72d62471e3d16b.png)
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3 . 已知正实数a、b、c满足
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f9a67d0c6387f646e9041cc37ef63d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a4491efe17eb84a30ebdcff8bec845.png)
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4 . 设
为正实数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05927e816fc834465ccf3cecced8d510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25ef3da55b7121ead49f7d8aea01443.png)
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5 . 设
为非负实数,满足
.求
的最小值和最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7169ce3255d2a02a20aa5932d2bd48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a399a276e30510e557b42ee5db5510b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635e18bfef2e7514cfacf088e55b95e6.png)
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6 . 设
,记:
,其中求和是对1,2,…,n的所有
个k元组合
进行的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0610af5abf3cc278643f5696f58b625d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b645e448faf42a5eec1a1e02b85325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c015bd3b114c45ca0881c8468b4b35d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800cc73c3cf1e852b3cb2eb9dc1ff3f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663211001b3f08bcbe2cf4a9c9ee0505.png)
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7 . 设
,
(
为常数).若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6694500d0b3cd2784e4c9617d2d77861.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ff6ff5c00396b7f7d50675d80a0844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700458c01a7ad031e27d80ed43e9e882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57db73d5e95d0dda392d5af3a5cecaa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cb85820577e4c835a8d6a2f272ebd0.png)
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8 . 已知实数
、b、c满足
,求
的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f9223bc24df8d429d743692fff7c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7ca97c9b586e1c83cad6b9078e84cc.png)
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9 . 设
为实数,且
.则
的最大值等于.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c27a9af7db04a611063978a7990745e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1df8c43c7d38402c0807b717c6ea4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ef4ab5ad39ce3c6907af62c9cf209f.png)
A.![]() | B.0 | C.![]() | D.![]() |
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