Help!

BrownianMan · #1 $Old$ October 22nd, 2009, 10:03 AM

Prove the following result:

A triangle with sides that can be written in the form n^2+1,n^2-1, and 2(where n>1) is right-angled. Show by means of a counterexample, that the converse is false.

---------------------------------

I am not sure how to do this!

proscientia · #2 $Old$ October 22nd, 2009, 10:32 AM

The third side should be $2n,$ not $2.$

As $\left(n^2+1\right)^2=\left(n^2-1\right)^2+\left(2n\right)^2,$ the triangle is right-angled by Pythagoras. For a counterexample, consider a triangle with sides $5,12,13.$