+52 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.
