For positive non-zero real variables $x$ and $y$, if $$\ln\left(\frac{x + y}{2}\right) = \frac{1}{2} [\ln(x) + \ln(y)]$$ then, the value of $\frac{x}{y} + \frac{y}{x}$ is

Given the equation:

Using logarithmic properties $\ln(a) + \ln(b) = \ln(ab)$ and $k\ln(a) = \ln(a^k)$:

Exponentiating both sides:

Rearranging gives:

Thus, $\sqrt{x} = \sqrt{y} \implies x = y$.

Now, evaluating the expression:

Hence, the correct option is (C).