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estudier
Group Title
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)
 2 years ago
 2 years ago
estudier Group Title
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)
 2 years ago
 2 years ago

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

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

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

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

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

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

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

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

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

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

estudier Group TitleBest 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
 2 years ago

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

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

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

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

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

estudier Group TitleBest ResponseYou've already chosen the best response.1
If 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
 2 years ago

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

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

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

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

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

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