Question 23
a. Determine the largest possible value $M$ that $x+y+z$ can take if $x$, $y$ and $z$ are positive real numbers with
$$
16xyz = (x + y)^2(x + z)^2.
$$
b. Show that there are infinitely many triples $(x, y, z)$ of positive rational numbers for which
$$
16xyz = (x + y)^2(x + z)^2 \text{ and } x + y + z = M
$$
hold.
$$
16xyz = (x + y)^2(x + z)^2.
$$
b. Show that there are infinitely many triples $(x, y, z)$ of positive rational numbers for which
$$
16xyz = (x + y)^2(x + z)^2 \text{ and } x + y + z = M
$$
hold.