SOLUTION: For the equation (a-b)^2 + a^2 = 625, a and b are integers and a≥0. List the ordered pairs that occur.

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Question 1209332: For the equation (a-b)^2 + a^2 = 625, a and b are integers and a≥0. List the ordered pairs that occur.
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The (unordered) pairs of non-negative integers m and n that satisfy the equation m^2+n^2 = 625 are (0,25), (7,24), and (15,20).

In this problem we need to have (a-b)^2+a^2 = 625, with a greater than or equal to 0.

So a can be any of the six numbers in those unordered pairs; and, since (a-b) is squared, (a-b) can be positive or negative.

    a  (a-b)  b  ordered pair (a,b)
  ----------------------------------
    0   25  -25  (0,-25)
    0  -25   25  (0,25)
    7   24  -17  (7,-17)
    7  -24   31  (7,31)
   15   20   -5  (15,-5)
   15  -20   35  (15,35)
   20   15    5  (20,5)
   20  -15   35  (20,35)
   24    7   17  (24,17)
   24   -7   31  (24,31)
   25    0   25  (25,0)
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