RMO 2025 Problem 2

Let $a$ , $b$ , $c$ be distinct non-zero real numbers satisfying $a+\frac{2}{b}= b+\frac{2}{c}=c+\frac{2}{a}$ Determine the value of $|a^2 b+b^2 c+c^2 a|$ Proposed by Prof. B.J. Venkatachala