【答案】
分析:(1)把原式的第一項(xiàng)的被開方數(shù)變形為
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/0.png)
x,第二項(xiàng)的被開方數(shù)變形為4
2x,第三項(xiàng)的被開方數(shù)變形為3
2x,利用二次根式的化簡(jiǎn)公式
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/1.png)
=|a|進(jìn)行變形,合并同類二次根式即可得到結(jié)果;
(2)找出一元二次方程中的二次項(xiàng)系數(shù)a,一次項(xiàng)系數(shù)b,以及常數(shù)項(xiàng)c,計(jì)算出根的判別式,由根的判別式大于0,得到原方程有兩個(gè)不相等的實(shí)數(shù)根,然后把a(bǔ),b及c的值代入求根公式,即可求出原方程的解;
(3)把原式先利用去括號(hào)法則去括號(hào)后,找出同類項(xiàng),合并同類項(xiàng)后,得到原式的最簡(jiǎn)形式,將a的值代入即可求出值.
解答:解:(1)原式=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/2.png)
…(3分)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/3.png)
…(5分)
(2)x
2+2x-5=0,
∵a=1,b=2,c=-5,
∴b
2-4ac=4+20=24>0,
∴
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/4.png)
,…(3分)(△算對(duì)獨(dú)立給1分)
∴x
1=-1+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/5.png)
,x
2=-1-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/6.png)
;…(5分)(各1分)
(3)2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/7.png)
=2a-2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/8.png)
+a+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/9.png)
-a
2+3a+4
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/10.png)
,…(4分)(對(duì)一項(xiàng)給1分)
∵a=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/11.png)
,∴
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/12.png)
,
∴原式=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/13.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164700129967934/SYS201310221647001299679017_DA/14.png)
.…(6分)(對(duì)一項(xiàng)給1分)
點(diǎn)評(píng):此題考查了二次根式的化簡(jiǎn)求值,一元二次方程的解法,以及二次根式的加減運(yùn)算,其中利用公式法解一元二次方程的步驟為:先把方程整理為一般形式,找出a,b,c,然后計(jì)算出b
2-4ac,由b
2-4ac的符號(hào)判斷方程根的情況,再利用求根公式來(lái)求解,作第三小題時(shí),應(yīng)將原式化為最簡(jiǎn)再代值.