Let \(\displaystyle f(x) = \sqrt{\lim_{r \to x} \left\{ \frac{2r^2 \Big[ (f(r)^2 - f(x)f(r) \Big]}{r^2 - x^2} - r^3 e^{\dfrac{f(r)}{r}} \right\}}\) be differentiable in \((-\infty,0)\cup(0,\infty)\) and \( f(x)=1 \). Then the value of \( e a \), such that \( f(a)=0 \), is equal to: _________.
