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} +

Find an ordered triple (x,y,z) of real numbers satisfying \(x\le y\le z\) and the system of equations

 

\(\begin{align*} \sqrt{x} + \sqrt{y} + \sqrt{z} &= 10, \\ x + y + z &= 38, \\ \sqrt{xy} + \sqrt{xz} + \sqrt{yz} &= 30, \end{align*}\)