Problem

Source: 2018 China North Mathematical Olympiad Grade 10 Test 1 P2

Tags: inequalities, China, three variable inequality



Let $a$,$b$,$c$ be nonnegative reals such that $$a^2+b^2+c^2+ab+\frac{2}{3}ac+\frac{4}{3}bc=1$$Find the maximum and minimum value of $a+b+c$.