题目内容
按照指定方法解下列方程:(1)3x2-15=0 (用直接开平方法)
(2)x2-8x+15=0 (用因式分解法)
(3)x2-6x+7=0 (用配方法)
(4)y2+2=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200900866099212/SYS201311032009008660992019_ST/0.png)
【答案】分析:(1)把15移到右边,两边同时除以3,然后直接开平方求根;(2)用十字相乘法因式分解求出方程的根;(3)二次项系数是1,一次项系数是6,把7移到右边,用配方法解方程;(4)把右边的项移到左边,用求根公式求出方程的根.
解答:解:(1)x2=5,
∴x=±
.
(2)(x-3)(x-5)=0
∴x1=3,x2=5.
(3)x2-6x=-7
x2-6x+9=2
(x-3)2=2
x-3=±![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200900866099212/SYS201311032009008660992019_DA/1.png)
∴x=3±
.
(4)y2-2
y+2=0
△=8-8=0
y1=y2=![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200900866099212/SYS201311032009008660992019_DA/4.png)
点评:本题考查的是解一元二次方程,根据题目的不同特点,选择适当的方法解方程.
解答:解:(1)x2=5,
∴x=±
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200900866099212/SYS201311032009008660992019_DA/0.png)
(2)(x-3)(x-5)=0
∴x1=3,x2=5.
(3)x2-6x=-7
x2-6x+9=2
(x-3)2=2
x-3=±
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200900866099212/SYS201311032009008660992019_DA/1.png)
∴x=3±
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200900866099212/SYS201311032009008660992019_DA/2.png)
(4)y2-2
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200900866099212/SYS201311032009008660992019_DA/3.png)
△=8-8=0
y1=y2=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200900866099212/SYS201311032009008660992019_DA/4.png)
点评:本题考查的是解一元二次方程,根据题目的不同特点,选择适当的方法解方程.
![](http://thumb2018.1010pic.com/images/loading.gif)
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