Question 143
a. Determine the minimal value of
$$
\left(x+\frac{1}{y}\right)\left(x+\frac{1}{y}-2018\right)+\left(y+\frac{1}{x}\right)\left(y+\frac{1}{x}-2018\right)
$$
where $x$ and $y$ vary over the positive reals.
b. Determine the minimal value of
$$
\left(x+\frac{1}{y}\right)\left(x+\frac{1}{y}+2018\right)+\left(y+\frac{1}{x}\right)\left(y+\frac{1}{x}+2018\right)
$$
where $x$ and $y$ vary over the positive reals.
$$
\left(x+\frac{1}{y}\right)\left(x+\frac{1}{y}-2018\right)+\left(y+\frac{1}{x}\right)\left(y+\frac{1}{x}-2018\right)
$$
where $x$ and $y$ vary over the positive reals.
b. Determine the minimal value of
$$
\left(x+\frac{1}{y}\right)\left(x+\frac{1}{y}+2018\right)+\left(y+\frac{1}{x}\right)\left(y+\frac{1}{x}+2018\right)
$$
where $x$ and $y$ vary over the positive reals.