MathNet 2020 — Math Olympiad Vault — Part 01 Question 120

Suppose $a, b \gt 0$. The equation $\sqrt{|x|} + \sqrt{|x+a|} = b$ for $x$ has exactly three different real solutions, namely $x_1, x_2, x_3$, and $x_1 \lt x_2 \lt x_3 = b$. Then the value of $a+b$ is ______.