【答案】
分析:要证原不等式成立,只要证
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/0.png)
<
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/1.png)
,即证9+2
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/2.png)
<9+2
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/3.png)
,故只要证
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/4.png)
<
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/5.png)
,即证14<18,此种证明方法是分析法.
解答:解:要证明不等式
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/6.png)
,只要证
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/7.png)
<
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/8.png)
,即证9+2
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/9.png)
<9+2
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/10.png)
,
故只要证
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/11.png)
<
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103173759636782607/SYS201311031737596367826007_DA/12.png)
,即证14<18.
以上证明不等式所用的最适合的方法是分析法.
故选B.
点评:本题考查的是分析法和综合法,解答此题的关键是熟知比较大小的方法.从求证的不等式出发,“由果索因”,逆向逐步找这个不等式成立需要具备的充分条件,分析法──通过对事物原因或结果的周密分析,从而证明论点的正确性、合理性的论证方法.也称为因果分析,属于中档题.