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):
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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)
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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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