Question 36
Let $x_1, x_2, \dots, x_9$ be nonnegative real numbers satisfying
$$
x_1^2 + x_2^2 + \dots + x_9^2 \geq 25.
$$
*Prove that there exist three of these numbers with a sum of at least 5.*
$$
x_1^2 + x_2^2 + \dots + x_9^2 \geq 25.
$$
*Prove that there exist three of these numbers with a sum of at least 5.*