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对于问题:“已知两个正数x,y满足x+y=2,求的最小值”,给出如下一种解法: ...
对于问题:“已知两个正数x,y满足x+y=2,求
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124224241191684/SYS201310251242242411916010_ST/0.png)
的最小值”,给出如下一种解法:
Qx+y=2,∴
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124224241191684/SYS201310251242242411916010_ST/1.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124224241191684/SYS201310251242242411916010_ST/2.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124224241191684/SYS201310251242242411916010_ST/3.png)
,
Qx>0,y>0,∴
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124224241191684/SYS201310251242242411916010_ST/4.png)
,∴
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124224241191684/SYS201310251242242411916010_ST/5.png)
,
当且仅当
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124224241191684/SYS201310251242242411916010_ST/6.png)
,即
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124224241191684/SYS201310251242242411916010_ST/7.png)
时,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124224241191684/SYS201310251242242411916010_ST/8.png)
取最小值
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124224241191684/SYS201310251242242411916010_ST/9.png)
.
参考上述解法,已知A,B,C是△ABC的三个内角,则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124224241191684/SYS201310251242242411916010_ST/10.png)
的最小值为
.
考点分析:
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