Let f(x)=√(lim_r → x{(2 r^2[(f(r))^2-f(x) f(r)])/(r^2-x^2)-r^3 e^((f(r))/r)}) be differentiable in (-∞, 0) ∪(0, ∞) and f(1)=1. Then the value of e a,…

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