SOLUTION: The general formula for Pythagorean triples is {{{ a=m^2 - n^2 }}}, {{{ b=2mn }}}, and {{{ c=m^2 + n^2 }}} for integers m and n. Use the formula to find all the primitive Pythagore

Algebra ->  Pythagorean-theorem -> SOLUTION: The general formula for Pythagorean triples is {{{ a=m^2 - n^2 }}}, {{{ b=2mn }}}, and {{{ c=m^2 + n^2 }}} for integers m and n. Use the formula to find all the primitive Pythagore      Log On


   

Question 1055337: The general formula for Pythagorean triples is +a=m%5E2+-+n%5E2+, +b=2mn+, and +c=m%5E2+%2B+n%5E2+ for integers m and n. Use the formula to find all the primitive Pythagorean triples containing 24 as one number.
Found 2 solutions by CubeyThePenguin, ikleyn:
Answer by CubeyThePenguin(3113) About Me  (Show Source):
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The general formula for Pythagorean triples is +a=m%5E2+-+n%5E2+, +b=2mn+, and +c=m%5E2+%2B+n%5E2+ for integers m and n.
Use the formula to find all the primitive Pythagorean triples containing 24 as one number.
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24 = 2mn ----> mn = 24/2 = 12  ----> 


     (m,n) = (1,12)  gives the Pythagorean triple  (24,143,145).


     (m,n) = (3,4)   gives the Pythagorean triple  (7,24,25).


There no other primitive Pythagoren triples.


Solved, answered and explained.

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See also this web-page

https://en.wikipedia.org/wiki/Pythagorean_triple