Question 91
Positive real numbers $x, y$ satisfy the following condition: there exist $a \in [0, x], b \in [0, y]$ such that
$$
a^2 + y^2 = 2, \quad b^2 + x^2 = 1, \quad ax + by = 1.
$$
Then the maximum of $x+y$ is ______.
$$
a^2 + y^2 = 2, \quad b^2 + x^2 = 1, \quad ax + by = 1.
$$
Then the maximum of $x+y$ is ______.