+179 Let x and y be positive real numbers. Find the minimum value of
\(\left( x + \frac{1}{y} \right) \left( x + \frac{1}{y} - 2018 \right) + \left( y + \frac{1}{x} \right) \left( y + \frac{1}{x} - 2018 \right).\)
I really do not know where to start without involving huge expressions.
Naturally, however, if you could write \(y+\frac{1}{x}\) in terms of \(x+\frac{1}{y}\), or vice versa, that would really help.
Thanks for any replies!
