KöMaL 2026 C1912

Let $a_1, a_2, \ldots a_{10}$ be positive, not necessarily distinct numbers such that their sum is 95. Prove that $a_1^2+a_2^2+a_3^2+a_4^2+a_5^2+a_6^2+a_7^2+a_8^2+a_9^2+a_{10}^2 \geq 905$. When does the equality hold?