RMO Question

Algebra Level 3

\[\large A=\dfrac{a^2+1}{b+c}+\dfrac{b^2+1}{c+a}+\dfrac{c^2+1}{a+b}\]

If \(a\),\(b\), and \(c\) are three positive real numbers, then find the minimum value of \(A\).

Source: RMO.