【答案】
分析:(1)利用直接開平方法求解此一元二次方程即可求得答案;
(2)此題利用配方法求解此一元二次方程即可求得答案;
(3)首先整理為一般式,然后利用公式法求解此一元二次方程即可求得答案;
(4)首先化為一般式,然后利用因式分解法求解此一元二次方程即可求得答案;
(5)此題利用配方法求解此一元二次方程即可求得答案;
(6)此題利用配方法求解此一元二次方程即可求得答案;
(7)首先化為一般式,然后利用因式分解法求解此一元二次方程即可求得答案.
解答:解:(1)∴
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/0.png)
x+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/1.png)
=±3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/2.png)
,
∴x=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/3.png)
或x=2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/4.png)
,
∴原方程的根為:x
1=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/5.png)
,x
2=2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/6.png)
;
(2)∵2x
2+x-6=0,
∴x
2+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/7.png)
x=3,
∴(x+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/8.png)
)
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/9.png)
,
∴x+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/10.png)
=±
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/11.png)
,
∴原方程的根為x
1=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/12.png)
,x
2=-2;
(3)化簡(jiǎn)得:3x
2+10x+5=0,
∴a=3,b=10,c=5,
∴△=b
2-4ac=100-60=40,
∴x=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/13.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/14.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/15.png)
,
∴原方程的根為:x
1=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/16.png)
,x
2=-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/17.png)
;
(4)∵x(x+1)=12,
∴x
2+x-12=0,
∴(x+4)(x-3)=0,
∴x+4=0或x-3=0,
∴原方程的根為:x
1=-4,x
2=3;
(5)∵x
2-2x-399=0,
∴x
2-2x=399,
∴(x-1)
2=400,
∴x-1=±20,
∴原方程的根為:x
1=21,x
2=-19;
(6)∵x
2-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/18.png)
x-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/19.png)
=0,
∴x
2-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/20.png)
x=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/21.png)
,
∴(x-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/22.png)
)
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/23.png)
,
∴x-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/24.png)
=±
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/25.png)
,
∴原方程的根為:x
1=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/26.png)
,x
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/27.png)
;
(7)∵x
2+mx+2=mx
2+3x,
∴(m-1)x
2+(3-m)x-2=0,
∴(x-1)[(m-1)x+2]=0,
∴x-1=0或(m-1)x+2=0,
∴原方程的根為:x
1=1,x
2=-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103195819425337081/SYS201311031958194253370028_DA/28.png)
.
點(diǎn)評(píng):此題考查了一元二次方程的解法.題目比較簡(jiǎn)單,解題需細(xì)心,解題的關(guān)鍵是注意選擇適宜的解題方法.