Let n be a positive integer and x a real number with x $\ge$ $\frac {3n^2+1}{3}$. Calculate $\lfloor \sqrt{x^2-nx}+\sqrt{x^2-n^2}+\sqrt{x^2+n^2}-3x \rfloor$, where $\lfloor t \rfloor$ is the usual notation for the integer part of t.
I have proved that the expression is negative using the mean inequality and I have seen that the result depends on n and x, so it isn't something constant. I tried to fit every radical between 2 expressions, but I couldn't do it for the last one. Can you help me?