【答案】
分析:(1)先把
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/0.png)
,
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/1.png)
化為最簡二次根式,再把3-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/2.png)
提
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/3.png)
出來,變?yōu)?img src="http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/4.png">(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/5.png)
-1),然后把
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/6.png)
乘到后面括號內(nèi),再利用平方差公式去括號,最后進行合并即可;
(2)非0的0次冪為1,
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/7.png)
可化為2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/8.png)
;
(3)先把-2移到方程右邊,然后方程兩邊除以2,方程化為:x
2-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/9.png)
x=1,接著方程兩邊同時加上(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/10.png)
)
2,使方程左邊變?yōu)橐粋€完全平方式,最后用直接開平方法解即可.
(4)把左邊寫成完全平方式:(x-3)
2,然后用直接開平方法求解;
(5)先移項變形為:(x-5)
2-2(x-5)=0,然后用因式分解法求解.
解答:解:(1)原式=4
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/11.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/12.png)
+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/13.png)
(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/14.png)
-1)(1+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/15.png)
),
=4
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/16.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/17.png)
+(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/18.png)
-1)(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/19.png)
+1),
=4
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/20.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/21.png)
+(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/22.png)
)
2-1,
=4
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/23.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/24.png)
+2;
(2)原式=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/25.png)
-1+2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/26.png)
-2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/27.png)
,
=-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/28.png)
;
(3)移項,得2x
2-7x=2,
方程兩邊除以2,得x
2-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/29.png)
x=1,
方程兩邊同時加上(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/30.png)
)
2,得(x-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/31.png)
)
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/32.png)
,
∴x-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/33.png)
=±
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/34.png)
,
∴x
1=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/35.png)
,x
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/36.png)
;
(3)方程變形為:(x-3)
2=(5-2x)
2,
∴x-3=±(5-2x),
即x-3=5-2x或x-3=-(5-2x),
∴x
1=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194638738658028/SYS201311031946387386580018_DA/37.png)
,x
2=2;
(5)移項變形為:(x-5)
2-2(x-5)=0,
∴(x-5)(x-5-2)=0,
即x-5=0或x-5-2=0,
∴x
1=5,x
2=7.
點評:本題考查了一元二次方程ax
2+bx+c=0(a≠0,a,b,c為常數(shù))的解法.解一元二次方程可采用直接開平方法,因式分解法和配方法等.其中用配方法時要先把二次項系數(shù)變?yōu)?,然后加上一次項系數(shù)一半的平方,配成完全平方式,再用直接開平方法求解;也考查了二次根式的混合運算.