解题方法
1 . 若
,
,
,
,
均为正数,则有
二元均值不等式:
,当且仅当
时取等号;
三元均值不等式:
,当且仅当
时取等号;
四元均值不等式:
,当且仅当
时取等号.
(1)猜想
元均值不等式;
(2)若
,
,
均为正数,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
二元均值不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ac5bcc086eddd5cd7d85b8b85b8d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b2fb1017d5dfe3a300de3e14a71b6f.png)
三元均值不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb2daa924ce81a49c4f2c097a37db9c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3628a3eef8edc8dafbb942c00bb003.png)
四元均值不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66985785aa702ab35a367fdcdfb5e78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f781f388a0c97838a2445e7600ad3294.png)
(1)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](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/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb603414e6b47ce46dbbcd3f955a424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e823000035b4482d4868da22c0f9fc7.png)
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