阅读材料:小明在学习二次根式后,发现一些含根号的式子可以写成另一个式子的平方,如:3+2
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717613344.png)
=(1+
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717613344.png)
)
2,善于思考的小明进行了以下探索:
设a+b
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717613344.png)
=(m+n
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717613344.png)
)
2(其中a、b、m、n均为整数),则有a+b
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717613344.png)
=m
2+2n
2+2mn
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717613344.png)
.
∴a=m
2+2n
2,b=2mn.这样小明就找到了一种把部分a+b
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717613344.png)
的式子化为平方式的方法.
请你仿照小明的方法探索并解决下列问题:
(1)当a、b、m、n均为正整数时,若a+b
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717706344.png)
=(m+n
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717706344.png)
)
2,用含m、n的式子分别表示a、b,得a=________,b=________;
(2)利用所探索的结论,找一组正整数a、b、m、n,填空:________+________
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717706344.png)
=(______+______
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717706344.png)
)
2;
(3)若a+4
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717706344.png)
=(m+n
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823032717706344.png)
)
2,且a、m、n均为正整数,求a的值.