解方程:
(1)2x2-5x-1=0(配方法)
(2)3y(y-1)=2(y-1)
【答案】
分析:(1)把左邊配成完全平方式,右邊化成常數(shù),再開方;(2)先移項,再用提公因式法進(jìn)行因式分解.
解答:解:(1)系數(shù)化為1得,x
2-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/0.png)
x-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/1.png)
=0,
移項得,x
2-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/2.png)
x=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/3.png)
,
兩邊加
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/4.png)
得,x
2-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/5.png)
x+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/6.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/7.png)
+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/8.png)
,
即:(x-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/9.png)
)
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/10.png)
,
x-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/11.png)
=±
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/12.png)
,
x=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/13.png)
,
x
1=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/14.png)
,x
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/15.png)
.
(2)3y(y-1)=2(y-1)
移向得,3y(y-1)-2(y-1)=0,
提公因式得,(y-1)(3y-2)=0,
解得y-1=0或3y-2=0,
y
1=1,y
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103194752787465290/SYS201311031947527874652016_DA/16.png)
.
點評:(1)配方時要注意配方的方法,當(dāng)二次項系數(shù)是1時,方程兩邊加上一次項系數(shù)一半的平方;
(2)本題注意到方程左右兩邊有公因式y(tǒng)-1,是解題的關(guān)鍵.