Question 85
Let $a, b, x, y$ be non-negative numbers, $k \gt 0$ and for these numbers the following inequalities are true:
$$
a + kx \le 1; \quad a + ky \le 1; \quad b + \frac{x}{k} \le 1; \quad b + \frac{y}{k} \le 1.
$$
Prove that the following inequality is true:
$$
(a + x)^2 + (b + y)^2 \le 2.
$$
$$
a + kx \le 1; \quad a + ky \le 1; \quad b + \frac{x}{k} \le 1; \quad b + \frac{y}{k} \le 1.
$$
Prove that the following inequality is true:
$$
(a + x)^2 + (b + y)^2 \le 2.
$$