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Math Help - Help!

  1. #1
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    Help!

    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.

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    I am not sure how to do this!
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  2. #2
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    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.
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