Is it geometry?

Geometry Level 4

\[\begin{cases} { x }^{ 2 }+{ y }^{ 2 }={ z }^{ 2 } \\ { y }^{ 2 }-yz+{ z }^{ 2 }={ x }^{ 2 } \\ { z }^{ 2 }+k·zx+{ x }^{ 2 }={ y }^{ 2 } \end{cases}\]

Let \(x\),\(y\),\(z\) positive numbers the satisfy the system of equations above.

If this system has at least one solution, what is the value of \(k\)?

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