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estudier

  • 2 years ago

Find all Pythagorean triples with 3 sides in in arithmetic progression?

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  1. Cheese3.1416
    • 2 years ago
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    I know what a Pythagorean triple is, but what do you mean by one having three sides?

  2. estudier
    • 2 years ago
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    Right triangle with Pythagorean triple is a Pythagorean triangle

  3. estudier
    • 2 years ago
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    Think of it as a bit of a hint....

  4. AbhimanyuPudi
    • 2 years ago
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    3,4,5 the basic thing!! let me think about the rest

  5. AbhimanyuPudi
    • 2 years ago
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    Ofcourse by 3,4,5 I also mean all such triplets..6,8,10 ; 9,12,15 etc

  6. AbhimanyuPudi
    • 2 years ago
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    I think there are no more except the 3-4-5 forms

  7. estudier
    • 2 years ago
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    Thinking is good, a proof would be better...:-)

  8. estudier
    • 2 years ago
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    Hint?

  9. AbhimanyuPudi
    • 2 years ago
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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

  10. estudier
    • 2 years ago
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    That will do....

  11. AbhimanyuPudi
    • 2 years ago
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    :-)

  12. estudier
    • 2 years ago
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    x^2 + (x+d)^2 = (x+2d)^2 -> x^2 -2xd -3d^2 = 0 -> (x-3d)(x+d) = 0 etc.....

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