Problem

Source: 2018 Taiwan TST Round 1

Tags: inequalities



Assume $ a,b,c $ are arbitrary reals such that $ a+b+c = 0 $. Show that $$ \frac{33a^2-a}{33a^2+1}+\frac{33b^2-b}{33b^2+1}+\frac{33c^2-c}{33c^2+1} \ge 0 $$