Problem

Source: Mathcenter Contest / Oly - Thai Forum 2012 (R1) p6 sl-14 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

Tags: algebra, inequalities, max



For a real number $a,b,c>0$ where $bc-ca-ab=1$ find the maximum value of $$P=\frac{4024}{1+a^2}-\frac{4024}{1+b^2}-\frac{2555}{1+c^2}$$and find out when that holds . (PP-nine)