SOLUTION: sqrt(a^2+b^2)=613 (a+b)= ?

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Question 1054179: sqrt(a^2+b^2)=613
(a+b)= ?
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
We will find out if (a,b,613) is a Pythagorean triple.

If so then (a,b,613) = (m²-n²,2mn,m²+n²)

b+613 = 2mn+m²+n²
b+613 = m²+2mn+n²
b+613 = (m+n)²

We find the next perfect square greater than 613,
and see if that works. √613 = 24.7588...

So the next perfect square is 25² = 625

If b+613 = 625
       b = 612

Then a=sqrt%28613%5E2-612%5E2%29=sqrt%28375769-374544%29=sqrt%281225%29=35

So it works, and a+b = 35+612 = 647 

Edwin