Question 97
Positive real numbers $a$, $b$, $c$, $d$ satisfy equalities
$$
a = c + \frac{1}{d} \quad \text{and} \quad b = d + \frac{1}{c}.
$$
Prove an inequality $ab \ge 4$ and find a minimum of $ab + cd$.
$$
a = c + \frac{1}{d} \quad \text{and} \quad b = d + \frac{1}{c}.
$$
Prove an inequality $ab \ge 4$ and find a minimum of $ab + cd$.