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

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AbhimanyuPudi
 2 years ago
Best ResponseYou've already chosen the best response.0the 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

AbhimanyuPudi
 2 years ago
Best ResponseYou've already chosen the best response.0Its not generalised though!!

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1It's a start... Let's say we have x^2 + y^2 = z^2 and xy = 2n^2 (triangle area)

AbhimanyuPudi
 2 years ago
Best ResponseYou've already chosen the best response.0Okay so we take it as hypothesis and prove it a contradiction..I'll try

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1350135906515:dw

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1350136054246:dw

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1Promising...how will you get a quartic so as to use the given?

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1You need to multiply the first line of your first post with something...

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1Writing your first line in full: (x+y)^2 = x^2 + y^2 +2xy = z^2 + 4n^2

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1350136543480:dw

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1(x+y)^2 = x^2 + y^2 +2xy = z^2 + 4n^2 Your first line (xy)^2 = x^2 + y^2 2xy = z^2 4n^2

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1that would yield extra non dependent solution.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1*equation (solution)

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1We, are just trying to get a contradiction....

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1We are assuming a triangle that is square....

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1yeah ... three variables 3 non dependent equations ... it's possible to deduce from that.

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1If u multiply those two above, u get (x^2y^2)^2 = z^4  (2n)^4 which contradicts the given so no Pythagorean triangle area is square

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1yeah i see the trick!!

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1U almost had it, a bit more time, u would have had it, I think....

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1well .. I'm not too good with algebraic manipulations.

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1I shall put up a few more while it's stil quiet....

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1I usually takes quite lot more than necessary steps to do things.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1I might go offline for 2hrs ... well I would enjoy if you tag me in few interesting problems if you have.
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