Question 111
Let $a$, $b$, $c$ and $d$ be positive real numbers with $a + b + c + d = 2$. Prove that
$$
\frac{(a+c)^2}{ad+bc} + \frac{(b+d)^2}{ac+bd} + 4 \ge 4 \left( \frac{a+b+1}{c+d+1} + \frac{c+d+1}{a+b+1} \right).
$$
$$
\frac{(a+c)^2}{ad+bc} + \frac{(b+d)^2}{ac+bd} + 4 \ge 4 \left( \frac{a+b+1}{c+d+1} + \frac{c+d+1}{a+b+1} \right).
$$