Question 87
Consider non-negative real numbers $a, b, c$ satisfying the condition $a^2 + b^2 + c^2 = 2$. Find the maximum value of the following expression
$$
P = \frac{\sqrt{b^2 + c^2}}{3 - a} + \frac{\sqrt{c^2 + a^2}}{3 - b} + a + b - 2022c.
$$
$$
P = \frac{\sqrt{b^2 + c^2}}{3 - a} + \frac{\sqrt{c^2 + a^2}}{3 - b} + a + b - 2022c.
$$