Question 26
Prove that all real numbers $x \neq -1$, $y \neq -1$ with $xy = 1$ satisfy the following inequality:
$$
\left(\frac{2+x}{1+x}\right)^2 + \left(\frac{2+y}{1+y}\right)^2 \ge \frac{9}{2}
$$
$$
\left(\frac{2+x}{1+x}\right)^2 + \left(\frac{2+y}{1+y}\right)^2 \ge \frac{9}{2}
$$