SOLUTION: For the equation (a-b)^2+a^2=25, a and b are integers and a ≥ 0. List the ordered pairs that occur.

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Question 1105718: For the equation (a-b)^2+a^2=25, a and b are integers and a ≥ 0. List the ordered pairs that occur.
Found 2 solutions by Boreal, Edwin McCravy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
(a-b)^2=(25-a^2)
(a-b)=sqrt(25-a^2)
-b=-a+sqrt(25-a^2)
b=a-sqrt(25-a^2)
a can't be greater than 5, but a=5 b=0 works
a=4 b=1 works
a=3 and b=-1 works
a=2 and b can't be an integer
nor can a=1
a=0, b=5 works
(5, 0)
(0, -5)
(4, 1)
(3, -1)
Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!




We know the 3,4,5 right triangle 

That is, the Pythagorean triple (3,4,5)
where



and we know




So we have

 

which has solutions (a,b) = (4,1) or (4,7) 



which has solutions (a,b) = (3,-1) or (3,7) 



which has solutions (a,b) = (0,5) or (5,0) 



which has only solution (a,b) = (5,5) 

Edwin
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