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Find all Pythagorean triples with 3 sides in in arithmetic progression?
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Cheese3.1416
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I know what a Pythagorean triple is, but what do you mean by one having three sides?
estudier
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Right triangle with Pythagorean triple is a Pythagorean triangle
estudier
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Think of it as a bit of a hint....
AbhimanyuPudi
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3,4,5
the basic thing!! let me think about the rest
AbhimanyuPudi
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Ofcourse by 3,4,5 I also mean all such triplets..6,8,10 ; 9,12,15 etc
AbhimanyuPudi
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I think there are no more except the 3-4-5 forms
estudier
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Thinking is good, a proof would be better...:-)
estudier
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Hint?
AbhimanyuPudi
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(a+d)^2 = a^2 + (a-d)^2
Solving,
4d = a
Putting different values of d, we get different values of a..which are all multiples of 4.
a-d are respective multiples of 3
a+d are respective multples of 5
estudier
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That will do....
AbhimanyuPudi
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:-)
estudier
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x^2 + (x+d)^2 = (x+2d)^2 ->
x^2 -2xd -3d^2 = 0 ->
(x-3d)(x+d) = 0 etc.....