- anonymous

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)

- chestercat

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

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

- anonymous

Its not generalised though!!

- anonymous

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

Okay so we take it as hypothesis and prove it a contradiction..I'll try

- experimentX

|dw:1350135906515:dw|

- experimentX

|dw:1350136054246:dw|

- anonymous

Promising...how will you get a quartic so as to use the given?

- anonymous

You need to multiply the first line of your first post with something...

- anonymous

Writing your first line in full:
(x+y)^2 = x^2 + y^2 +2xy = z^2 + 4n^2

- experimentX

|dw:1350136543480:dw|

- anonymous

(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

- experimentX

oh!!

- anonymous

:-)

- experimentX

that would yield extra non dependent solution.

- experimentX

*equation (solution)

- anonymous

We, are just trying to get a contradiction....

- anonymous

We are assuming a triangle that is square....

- experimentX

yeah ... three variables 3 non dependent equations ... it's possible to deduce from that.

- anonymous

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

- experimentX

yeah i see the trick!!

- anonymous

U almost had it, a bit more time, u would have had it, I think....

- experimentX

well .. I'm not too good with algebraic manipulations.

- anonymous

I shall put up a few more while it's stil quiet....

- experimentX

I usually takes quite lot more than necessary steps to do things.

- experimentX

I might go offline for 2hrs ... well I would enjoy if you tag me in few interesting problems if you have.

- anonymous

Looking for something else?

Not the answer you are looking for? Search for more explanations.