题目内容
请阅读下列材料:我们规定一种运算:
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_ST/0.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_ST/1.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_ST/2.png)
(2)当x取何值时,
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_ST/3.png)
(3)若
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_ST/4.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_ST/5.png)
【答案】分析:(1)根据运算的规定,可知
=-1×0.5-(-2)×2,然后根据有理数的混合运算法则,得出结果;
(2)根据运算的规定,可知
=2x2-1×(0.5-x),从而可列出关于x的方程2x2-1×(0.5-x)=0,解这个方程,即可求出结果;
(3)根据运算的规定,可知
=3(0.5x-1)-8y,
=-x+0.5y,从而可列出方程组
,解这个方程组,即可求出x和y的值.
解答:解:(1)∵
=ad-bc,
∴
=-1×0.5-(-2)×2=-0.5+4=3.5;(2分)
(2)由题意,得2x2-1×(0.5-x)=0,(4分)
整理,得4x2+2x-1=0,
解之,得
.(5分)
∴当
或
时,
=0;
(3)∵
=ad-bc,
∴
=3(0.5x-1)-8y,
=-x+0.5y,
由题意,得组
,
解得
.
故x=8,y=2.(8分)
点评:本题考查学生读题做题的能力.关键是透彻理解题中运算的规定.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/0.png)
(2)根据运算的规定,可知
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/1.png)
(3)根据运算的规定,可知
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/3.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/4.png)
解答:解:(1)∵
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/5.png)
∴
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/6.png)
(2)由题意,得2x2-1×(0.5-x)=0,(4分)
整理,得4x2+2x-1=0,
解之,得
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/7.png)
∴当
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/8.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/9.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/10.png)
(3)∵
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/11.png)
∴
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/12.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/13.png)
由题意,得组
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/14.png)
解得
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022163144554383161/SYS201310221631445543831021_DA/15.png)
故x=8,y=2.(8分)
点评:本题考查学生读题做题的能力.关键是透彻理解题中运算的规定.
![](http://thumb2018.1010pic.com/images/loading.gif)
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