MathNet 2025 — 50 problems — Part 01 Question 21

Let $a$, $b$, and $c$ be real numbers such that $a^2(b + c) = 1$, $b^2(c + a) = 2$, and $c^2(a + b) = 5$. Given that there are three possible values for $abc$, compute the minimum possible value of $abc$.