Question 4
Let $x,$ $y,$ and $z$ be real numbers satisfying the system of equations $$
\begin{aligned} xy + 4z &= 60, \\ yz + 4x &= 60, \\ zx + 4y &= 60. \end{aligned}
$$
Let $S$ be the set of possible values of $x.$ Find the sum of the squares of the elements of $S.$
\begin{aligned} xy + 4z &= 60, \\ yz + 4x &= 60, \\ zx + 4y &= 60. \end{aligned}
$$
Let $S$ be the set of possible values of $x.$ Find the sum of the squares of the elements of $S.$