
Help!
Prove the following result:
A triangle with sides that can be written in the form n^2+1,n^21, and 2(where n>1) is rightangled. Show by means of a counterexample, that the converse is false.

I am not sure how to do this!

The third side should be $\displaystyle 2n,$ not $\displaystyle 2.$
As $\displaystyle \left(n^2+1\right)^2=\left(n^21\right)^2+\left(2n\right)^2,$ the triangle is rightangled by Pythagoras. For a counterexample, consider a triangle with sides $\displaystyle 5,12,13.$