Problem

Source: Indonesia MO 2022/8

Tags: inequalities, Hi, Indonesia, Indonesia MO



Determine the smallest positive real $K$ such that the inequality \[ K + \frac{a + b + c}{3} \ge (K + 1) \sqrt{\frac{a^2 + b^2 + c^2}{3}} \]holds for any real numbers $0 \le a,b,c \le 1$. Proposed by Fajar Yuliawan, Indonesia