Question 22
Let $a \gt 1$, $b \gt 1$, $c \gt 1$, $d \gt 1$, $x$, $y$ be real numbers satisfying
$$
a^x + b^y = (a^2 + b^2)^x \text{ and } c^x + d^y = 2^y (cd)^{y/2}.
$$
Prove that $x \lt y$.
$$
a^x + b^y = (a^2 + b^2)^x \text{ and } c^x + d^y = 2^y (cd)^{y/2}.
$$
Prove that $x \lt y$.