<p>Let <img alt="$x,y,$" height="11" src="https://latex.artofproblemsolving.com/6/9/2/692e3bee67c91837acbdcf63862b3b3c94366f28.png" width="32" /> and <img alt="$z$" height="10" src="https://latex.artofproblemsolving.com/b/1/3/b13f21416d84e13708696f34dea81026cda583c9.png" width="11" /> be real numbers satisfying the system of equations<img alt="\begin{align*} xy + 4z &= 60 \\ yz + 4x &= 60 \\ zx + 4y &= 60. \end{align*}" height="65" src="https://latex.artofproblemsolving.com/a/b/d/abd64d047b4dee2bfed719cb336c326182f1252e.png" width="105" />Let <img alt="$S$" height="14" src="https://latex.artofproblemsolving.com/a/d/2/ad28c83c99a8fd0dd2e2e594c9d02ee532765a0a.png" width="14" /> be the set of possible values of <img alt="$x.$" height="8" src="https://latex.artofproblemsolving.com/f/c/3/fc3be04db73828946870d3ccc6d122395a4bacf6.png" width="14" /> Find the sum of the squares of the elements of <img alt="$S.$" height="12" src="https://latex.artofproblemsolving.com/0/d/7/0d7e49ad93a99ed6dcafd1c6acba511a181ab6a4.png" width="14" /></p>

Question No: 394

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

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Tags: Algebra

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