题目内容
若正数m,n满足m+2n+4![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_ST/0.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_ST/1.png)
【答案】分析:先把m+2n+4
-6=3化为完全平方式的形式,再根据m,n是正整数求出
+2
的值,代入原式进行计算即可.
解答:解:∵正数m,n满足m+2n+4
-6=3,
∴(
+2
)2=9,
∵m,n是正整数,
∴
+2
=3,
∴原式=
=
.
故答案为:
.
点评:本题考查的是二次根式的化简求值,把已知代数式化为完全平方的形式是解答此题的关键.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_DA/0.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_DA/1.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_DA/2.png)
解答:解:∵正数m,n满足m+2n+4
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_DA/3.png)
∴(
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_DA/4.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_DA/5.png)
∵m,n是正整数,
∴
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_DA/6.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_DA/7.png)
∴原式=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_DA/8.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_DA/9.png)
故答案为:
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103195718076608804/SYS201311031957180766088006_DA/10.png)
点评:本题考查的是二次根式的化简求值,把已知代数式化为完全平方的形式是解答此题的关键.
![](http://thumb2018.1010pic.com/images/loading.gif)
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