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【330965】4.2 用配方法解一元二次方程 同步练习2

时间:2025-01-21 13:27:52 作者: 字数:1592字
简介:

4.2 用配方法解一元二次方程

一、填空题

1. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> =__________a2的平方根是__________.

2.用配方法解方程x2+2x1=0

移项得__________________

配方得__________________

即(x+__________2=__________

x+__________=__________x+__________=__________

x1=__________,x2=__________

3.用配方法解方程2x24x1=0

方程两边同时除以2__________

移项得__________________

配方得__________________

方程两边开方得__________________

x1=__________,x2=__________

二、解答题

1.将下列各方程写成(x+m)2=n的形式

1x22x+1=0

(2)x2+8x+4=0

(3)x2x+6=0

2.将下列方程两边同时乘以或除以适当的数,然后再写成(x+m)2=n的形式

(1)2x2+3x2=0



(2) <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> x2+x2=0




3.用配方法解下列方程

(1)x2+5x1=0 (2)2x24x1=0




(3)  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> x26x+3=0

参考答案

一、1.|a| ±a

2.x2+2x=1 x2+2x+1=1+1 1 1 1

0 2

3.x22x <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> =0 x22x= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> x22x+1= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> (x1)2= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> +1  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> +1

二、1.(1)解:(x1)2=0

(2)解:x2+8x=4

x2+8x+16=12

(x+4)2=12

(3)解:x2x=6

x2x+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> =5 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

(x <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> )2=5 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

2.(1)解:x2+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> x1=0

x2+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> x=1

x2+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> x+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> =1 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

(x+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> )2= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

(2)解:x2+4x8=0

x2+4x=8

x2+4x+4=12

(x+2)2=12

3.(1)解:x2+5x=1

x2+5x+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

(x+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> )2= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

x+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

x1= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

(2)解:x22x <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> =0

x22x= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

x22x+1= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

(x1)2= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

x1=± <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

x1= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> ,x2= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

(3)解:x224x+12=0

x224x=12

x224x+144=132

(x12)2=132

x12=±2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a>

x1=2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> +12,x2=2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/213/" title="方法" class="c1" target="_blank">方法</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/934/" title="配方" class="c1" target="_blank">配方</a> +12