解方程:
(1)(3x+2)2=24
(2)3x2-1=4x(公式法)
(3)(2x+1)2=3(2x+1)
(4)x2-2x-399=0(配方法)
【答案】
分析:(1)兩邊直接開平方,可將一元二次方程降次為兩個一元一次方程,求出方程的根;
(2)化成一般形式后用公式法解比較方便;
(3)把右邊的項移到左邊,用提公因式的方法因式分解解方程;
(4)二次項的系數(shù)是1,一次項的系數(shù)是-2,用配方法較簡單.
解答:解:(1)(3x+2)
2=24
兩邊直接開平方:3x+2=±
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103001117743054745/SYS201311030011177430547020_DA/0.png)
3x=-2±2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103001117743054745/SYS201311030011177430547020_DA/1.png)
x=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103001117743054745/SYS201311030011177430547020_DA/2.png)
∴x
1=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103001117743054745/SYS201311030011177430547020_DA/3.png)
,x
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103001117743054745/SYS201311030011177430547020_DA/4.png)
.
(2)3x
2-1=4x
化成一般形式為:3x
2-4x-1=0
a=3,b=-4,c=-1
b
2-4ac=16-4×3×(-1)=28
x=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103001117743054745/SYS201311030011177430547020_DA/5.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103001117743054745/SYS201311030011177430547020_DA/6.png)
∴x
1=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103001117743054745/SYS201311030011177430547020_DA/7.png)
,x
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103001117743054745/SYS201311030011177430547020_DA/8.png)
;
(3)(2x+1)
2=3(2x+1)
把右邊的項移到左邊得:(2x+1)
2-3(2x+1)=0
提公因式得:(2x+1)(2x+1-3)=0
2x+1=0或2x-2=0
∴x
1=-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103001117743054745/SYS201311030011177430547020_DA/9.png)
,x
2=1;
(4)x
2-2x-399=0
移項得:x
2-2x=399
配方得:(x-1)
2=400
直接開平方得:x-1=±20
x=1±20
∴x
1=21,x
2=-19.
點評:根據(jù)方程特點,尋找最佳方法解方程.