Find an ordered triple \((x,y,z)\) of real numbers satisfying \(x\le y\le z\) and the system of equations
\(\begin{align*}\sqrt{x} + \sqrt{y} + \sqrt{z} &= 10, \\x + y + z &= 38, \\\sqrt{xy} + \sqrt{xz} + \sqrt{yz} &= 30,\end{align*}\)
or, if there is no such triple, enter the word "none" as your answer.
