RMO Inequalities - 2

Algebra Level 2

\[\large \dfrac{(a^2b+b^2c+c^2a)(ab^2+bc^2+ca^2)}{a^2b^2c^2} \]

If \(a,b\) and \(c\) are positive real numbers then the minimum value of the expression above.

Try part 1 here and part 3 here.