Prove that for side-lengths of a triangle then prove that the following inequality holds ,
Note : The inequality as proposed originally holds for all positive reals….but
I amn’t good enough to solve it without the extra condition I have imposed.
For all positive reals ,
For all sidelengths of a triangle ,
By expanding the LHS and using Lemma 1 we only have to prove that –
Since they are side-lengths of a triangle , using Ravi’s Substitution ,
the inequality re-arranges to –
which is true by Lemma 2.
This completes the proof.