阅读材料:为解方程(x
2-1)
2-5(x
2-1)+4=0,我们可以将x
2-1看作一个整体,然后设x
2-1=y…①,
那么原方程可化为y
2-5y+4=0,
解得y
1=1,y
2=4.
当y=1时,x
2-1=1,∴x
2=2,∴x=±
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197028_ST/0.png)
;
当y=4时,x
2-1=4,∴x
2=5,∴x=±
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197028_ST/1.png)
,
故原方程的解为x
1=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197028_ST/2.png)
,x
2=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197028_ST/3.png)
,x
3=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197028_ST/4.png)
,x
4=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197028_ST/5.png)
.
解答问题:
(1)上述解题过程,在由原方程得到方程①的过程中,利用______法达到了解方程的目的,体现了转化的数学思想;
(2)请利用以上知识解方程x
4-x
2-6=0.
考点分析:
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阅读材料,解答问题.
材料:利用解二元以次方程组的代入消元法可解形如
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197027_ST/0.png)
的方程组.
如:由(2)得y=x-1,代入(1)消元得到关于x的方程:x
2-x+
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197027_ST/1.png)
=0,∴x
1=x
2=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197027_ST/2.png)
将x
1=x
2=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197027_ST/3.png)
代入y=x-1得y
1=y
2=-
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197027_ST/4.png)
,∴方程组的解为
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197027_ST/5.png)
.
请你用代入消元法解方程组
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131103100807919419781/SYS201311031008079194197027_ST/6.png)
.
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