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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)
 one year ago
 one year 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)
 one year ago
 one year ago

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AbhimanyuPudiBest 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
 one year ago

AbhimanyuPudiBest ResponseYou've already chosen the best response.0
Its not generalised though!!
 one year ago

estudierBest 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)
 one year ago

AbhimanyuPudiBest ResponseYou've already chosen the best response.0
Okay so we take it as hypothesis and prove it a contradiction..I'll try
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1350135906515:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1350136054246:dw
 one year ago

estudierBest ResponseYou've already chosen the best response.1
Promising...how will you get a quartic so as to use the given?
 one year ago

estudierBest ResponseYou've already chosen the best response.1
You need to multiply the first line of your first post with something...
 one year ago

estudierBest 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
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1350136543480:dw
 one year ago

estudierBest 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
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
that would yield extra non dependent solution.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
*equation (solution)
 one year ago

estudierBest ResponseYou've already chosen the best response.1
We, are just trying to get a contradiction....
 one year ago

estudierBest ResponseYou've already chosen the best response.1
We are assuming a triangle that is square....
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yeah ... three variables 3 non dependent equations ... it's possible to deduce from that.
 one year ago

estudierBest 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
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yeah i see the trick!!
 one year ago

estudierBest ResponseYou've already chosen the best response.1
U almost had it, a bit more time, u would have had it, I think....
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
well .. I'm not too good with algebraic manipulations.
 one year ago

estudierBest ResponseYou've already chosen the best response.1
I shall put up a few more while it's stil quiet....
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
I usually takes quite lot more than necessary steps to do things.
 one year ago

experimentXBest 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.
 one year ago
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