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

 

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

 May 29, 2022
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By symmetry, there are 6 solutions.

 May 29, 2022

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