解下列方程:
(1)(x-1)2=3(直接開(kāi)平方法)
(2)x2+4x-1=0(配方法)
(3)y2-2y-4=0(公式法)
(4)3(x-5)2=x(5-x)(因式分解法)
(5)(x+1)(x+8)=-12(適合的方法)
【答案】
分析:(1)利用直接開(kāi)平方法求解即可求得答案;
(2)首先移項(xiàng),然后配方,繼而求得答案;
(3)利用公式法求解即可求得答案;
(4)提取公因式(x-5),利用因式分解法求解即可求得答案;
(5)首先整理,然后利用十字相乘法分解因式,即利用因式分解法求解即可求得答案.
解答:解:(1)∵(x-1)
2=3,
∴x-1=±
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202433767267893/SYS201311032024337672678019_DA/0.png)
,
解得:x
1=1+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202433767267893/SYS201311032024337672678019_DA/1.png)
,x
2=1-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202433767267893/SYS201311032024337672678019_DA/2.png)
;
(2)∵x
2+4x-1=0,
∴x
2+4x=1,
∴x
2+4x+4=1+4,
∴(x+2)
2=5,
即x+2=±
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202433767267893/SYS201311032024337672678019_DA/3.png)
,
解得:x
1=-2+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202433767267893/SYS201311032024337672678019_DA/4.png)
,x
2=-2-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202433767267893/SYS201311032024337672678019_DA/5.png)
;
(3)∵a=1,b=-2,c=-4,
∴△=b
2-4ac=(-2)
2-4×1×(-4)=20,
∴x=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202433767267893/SYS201311032024337672678019_DA/6.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202433767267893/SYS201311032024337672678019_DA/7.png)
=1±
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202433767267893/SYS201311032024337672678019_DA/8.png)
,
解得:x
1=1+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202433767267893/SYS201311032024337672678019_DA/9.png)
,x
2=1-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202433767267893/SYS201311032024337672678019_DA/10.png)
;
(4)∵3(x-5)
2=x(5-x),
∴(x-5)(3x-15+x)=0,
即x-5=0或3x-15+x=0,
解得:x
1=5,x
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202433767267893/SYS201311032024337672678019_DA/11.png)
;
(5)∵(x+1)(x+8)=-12,
∴x
2+9x+8=-12,
∴x
2+9x+20=0,
∴(x+5)(x+4)=0,
即x+5=0或x+4=0,
解得:x
1=-5,x
2=-4.
點(diǎn)評(píng):此題考查了一元二次方程的解法.此題難度不大,注意按要求解題,注意選擇適宜的解題方法.