Question 33
a. Determine the maximum $M$ of $x + y + z$ where $x$, $y$ and $z$ are positive real numbers with
$$
16xyz = (x + y)^2(x + z)^2.
$$
b. Prove the existence of infinitely many triples $(x, y, z)$ of positive rational numbers that satisfy $16xyz = (x + y)^2(x + z)^2$ and $x + y + z = M$.
$$
16xyz = (x + y)^2(x + z)^2.
$$
b. Prove the existence of infinitely many triples $(x, y, z)$ of positive rational numbers that satisfy $16xyz = (x + y)^2(x + z)^2$ and $x + y + z = M$.