I input the following to mathematica...

$\displaystyle m>n>0, \ \ \ p>q>0, \ \ \ q=p-\sqrt{2p^2-(m^2+2mn-n^2)},$

$\displaystyle pq(p^2-q^2)>2mn(m^2-n^2)$

and part of the result is

$\displaystyle 0<n<-\sqrt{2}\sqrt{4\sqrt{3}m^2+7m^2}-2\sqrt{3}m-3m$

with $\displaystyle m>0$, surely the RHS must be negative, so how can $\displaystyle n$ be greater than zeroless than a negative number ?and