探索规律
观察下列各式及验证过程:n=2时有式①:
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334002_ST/0.png)
n=3时有式②:
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334002_ST/1.png)
式①验证:
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334002_ST/2.png)
式②验证:
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334002_ST/3.png)
(1)针对上述式①、式②的规律,请写出n=4时的式子;
(2)请写出满足上述规律的用n(n为任意自然数,且n≥2)表示的等式,并加以验证.
考点分析:
相关试题推荐
先阅读下列的解答过程,然后再解答:
形如
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/0.png)
的化简,只要我们找到两个数a、b,使a+b=m,ab=n,使得
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/1.png)
+
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/2.png)
=m,
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/3.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/4.png)
,那么便有:
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/5.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/6.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/7.png)
±
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/8.png)
(a>b).
例如:化简
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/9.png)
.
【解析】
首先把
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/10.png)
化为
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/11.png)
,这里m=7,n=12,由于4+3=7,4×3=12
即
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/12.png)
+
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/13.png)
=7,
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/14.png)
×
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/15.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/16.png)
∴
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/17.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/18.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/19.png)
=2+
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/20.png)
.
由上述例题的方法化简:
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334001_ST/21.png)
.
查看答案
计算:(1)
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334000_ST/0.png)
;
(2)
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334000_ST/1.png)
+(-1)
3-2×
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307833464/SYS201311031022343078334000_ST/2.png)
.
查看答案
如图,实数a、b在数轴上的位置,化简:
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103102234307692655/SYS201311031022343076926024_ST/0.png)
.
查看答案