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estudier

Show that area of Pythagorean triangle x,y,z cannot be square (U can use that a^4-b^4 = c^2 has no positive solution)

  • one year ago
  • one year ago

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  1. AbhimanyuPudi
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    the base and height of pythagorean triangle are 3d and 4d where d is a constant Area = 1/2 x 3d x 4d = 3d x 2d = 6d^2 this is never a square

    • one year ago
  2. AbhimanyuPudi
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    Its not generalised though!!

    • one year ago
  3. estudier
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    It's a start... Let's say we have x^2 + y^2 = z^2 and xy = 2n^2 (triangle area)

    • one year ago
  4. AbhimanyuPudi
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    Okay so we take it as hypothesis and prove it a contradiction..I'll try

    • one year ago
  5. experimentX
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    |dw:1350135906515:dw|

    • one year ago
  6. experimentX
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    |dw:1350136054246:dw|

    • one year ago
  7. estudier
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    Promising...how will you get a quartic so as to use the given?

    • one year ago
  8. estudier
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    You need to multiply the first line of your first post with something...

    • one year ago
  9. estudier
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    Writing your first line in full: (x+y)^2 = x^2 + y^2 +2xy = z^2 + 4n^2

    • one year ago
  10. experimentX
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    |dw:1350136543480:dw|

    • one year ago
  11. estudier
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    (x+y)^2 = x^2 + y^2 +2xy = z^2 + 4n^2 Your first line (x-y)^2 = x^2 + y^2 -2xy = z^2 -4n^2

    • one year ago
  12. experimentX
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    oh!!

    • one year ago
  13. estudier
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    :-)

    • one year ago
  14. experimentX
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    that would yield extra non dependent solution.

    • one year ago
  15. experimentX
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    *equation (solution)

    • one year ago
  16. estudier
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    We, are just trying to get a contradiction....

    • one year ago
  17. estudier
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    We are assuming a triangle that is square....

    • one year ago
  18. experimentX
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    yeah ... three variables 3 non dependent equations ... it's possible to deduce from that.

    • one year ago
  19. estudier
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    If u multiply those two above, u get (x^2-y^2)^2 = z^4 - (2n)^4 which contradicts the given so no Pythagorean triangle area is square

    • one year ago
  20. experimentX
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    yeah i see the trick!!

    • one year ago
  21. estudier
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    U almost had it, a bit more time, u would have had it, I think....

    • one year ago
  22. experimentX
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    well .. I'm not too good with algebraic manipulations.

    • one year ago
  23. estudier
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    I shall put up a few more while it's stil quiet....

    • one year ago
  24. experimentX
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    I usually takes quite lot more than necessary steps to do things.

    • one year ago
  25. experimentX
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    I might go offline for 2hrs ... well I would enjoy if you tag me in few interesting problems if you have.

    • one year ago
  26. estudier
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    <k

    • one year ago
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