A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 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)
anonymous
 3 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)

This Question is Closed

anonymous
 3 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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It's a start... Let's say we have x^2 + y^2 = z^2 and xy = 2n^2 (triangle area)

anonymous
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1350135906515:dw

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Promising...how will you get a quartic so as to use the given?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0You need to multiply the first line of your first post with something...

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Writing your first line in full: (x+y)^2 = x^2 + y^2 +2xy = z^2 + 4n^2

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0(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
 3 years ago
Best ResponseYou've already chosen the best response.1that would yield extra non dependent solution.

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0We, are just trying to get a contradiction....

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0We are assuming a triangle that is square....

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0If 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
 3 years ago
Best ResponseYou've already chosen the best response.1yeah i see the trick!!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0U almost had it, a bit more time, u would have had it, I think....

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I shall put up a few more while it's stil quiet....

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

experimentX
 3 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.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.