Problem

Source: Indonesian TST for IMO 2023 Stage 1: Test 4 - Algebra

Tags: algebra



Let $a_1, a_2, a_3, a_4, a_5$ be non-negative real numbers satisfied \[\sum_{k = 1}^{5} a_k = 20 \ \ \ \ \text{and} \ \ \ \ \sum_{k=1}^{5} a_k^2 = 100\]Find the minimum and maximum of $\text{max} \{a_1, a_2, a_3, a_4, a_5\}$