SOLUTION: For the equation {{{ (a-b)^2 + a^2 = 169 }}} a and b are integers, and a≥0. Find the number of different ordered pairs (a,b) that occur.

Algebra ->  Equations -> SOLUTION: For the equation {{{ (a-b)^2 + a^2 = 169 }}} a and b are integers, and a≥0. Find the number of different ordered pairs (a,b) that occur.      Log On


   



Question 1189240: For the equation +%28a-b%29%5E2+%2B+a%5E2+=+169+ a and b are integers, and a≥0. Find the number of different ordered pairs (a,b) that occur.
Found 2 solutions by Alan3354, pademin:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
For the equation +%28a-b%29%5E2+%2B+a%5E2+=+169+ a and b are integers, and a≥0. Find the number of different ordered pairs (a,b) that occur.
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+%28a-b%29%5E2+%2B+a%5E2+=+169+
5^2 + 12^2 = 169
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a = 12, b = 7
a = 5, b = -7
a = 0, b = 13
a = 0, b = -13
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Might be others, but I doubt it.

Answer by pademin(1) About Me  (Show Source):
You can put this solution on YOUR website!
There are 7 integer solutions in total.
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a = 0, b = -13
a = 0, b = 13
a = 5, b = -7
a = 5, b = 17
a = 12, b = 7
a = 12, b = 17
a = 13, b = 13