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 \(k\)?
by
Félix de Montemar