![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749431292.png)
是平面上一點,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749446516.png)
是平面上不共線三點,動點
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749493289.png)
滿足:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749509961.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749524705.png)
,已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749540488.png)
時,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749555531.png)
.則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749571666.png)
的最小值____________.
試題分析:由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749509961.png)
得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749618849.png)
,當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749540488.png)
時,由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749555531.png)
得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749665731.png)
,即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749696682.png)
,又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240257497111783.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240257497272361.png)
,
當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025749743437.png)
時上式有最小值為-2.
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