【答案】
分析:將已知等式左右兩邊利用乘法分配律去括號后,移項整理后得到一個二次三項式,利用式子相乘法分解因式后,根據(jù)兩數(shù)相乘積為0,兩因式中至少有一個為0,可得出x=y=0或x=9y,由x=y=0得到所求式子無意義,故x=9y,將x=9y代入所求式子中,化簡約分后即可得到所求式子的值.
解答:解:
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/0.png)
(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/1.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/2.png)
)=3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/3.png)
(5
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/4.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/5.png)
)
去括號得:(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/6.png)
)
2-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/7.png)
=15(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/8.png)
)
2-3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/9.png)
移項合并得:(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/10.png)
)
2+2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/11.png)
-15(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/12.png)
)
2=0,
因式分解得:(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/13.png)
-3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/14.png)
)(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/15.png)
+5
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/16.png)
)=0,
可得:
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/17.png)
-3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/18.png)
=0或
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/19.png)
+5
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/20.png)
=0,
若
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/21.png)
+5
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/22.png)
=0,可得出x=y=0,所求式子無意義;
∴
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/23.png)
-3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/24.png)
=0,即x=9y,
則
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/25.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/26.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022165106895725563/SYS201310221651068957255012_DA/27.png)
=3.
點評:此題考查了二次根式的化簡求值,其中靈活變換已知的等式,得出x與y的關(guān)系式是解本題的關(guān)鍵.