Question

If $2\log (x-y)=\log x+\log y$ then value of $\frac{x}{y}+\frac{y}{x}$

Answer 1

Given, $2\log (x-y)=\log x+\log y$

$\Rightarrow \log (x-y{)}^2=\log (xy)$

$\Rightarrow (x-y{)}^2=xy$

$\Rightarrow x^2+y^2-2xy=xy$

$\Rightarrow x^2+y^2=3xy$

$\Rightarrow \frac{x}{y}+\frac{y}{x}=3$