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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

  1. $1$
  2. $1 / 2$
  3. $2$
  4. $4$
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