(2000•金華)(1)計算:
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_ST/0.png)
(2)解方程組:
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_ST/1.png)
.
【答案】
分析:(1)把
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/0.png)
化簡后直接計算.
(2)先把①代入②再用平方法求解.
解答:解:(1)原式=(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/1.png)
-4
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/2.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/3.png)
)•2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/4.png)
+5
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/5.png)
=(-3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/6.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/7.png)
)•2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/8.png)
+5
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/9.png)
=-18-6
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/10.png)
+5
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/11.png)
=-18-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/12.png)
.
(2)把①代入②得,-2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/13.png)
=1-x,
兩邊平方,得4(x+2)=(1-x)
2,即x
2-6x-7=0,
解得x=7或x=-1,
把x=7代入原方程得,左邊=-2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/14.png)
=-6,右邊=1-7=-6,原方程成立;
把x=-1代入原方程得,左邊=-2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/15.png)
=-2,右邊=1+1=2,原方程不成立;
故x=-1是原方程的增根,∴x=7,
代入②得y=3,
故原方程組的解為
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131021232701573382946/SYS201310212327015733829027_DA/16.png)
.
點評:(1)在進行二次根式的計算時,要先把二次根式化為最簡二次根式,然后再計算;
(2)先把①代入②再用平方法求解.
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