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# Not sure how to solve this

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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*}

or, if there is no such triple, enter the word "none" as your answer.

May 25, 2021

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One triple that wrks is (4,9,25).

May 25, 2021
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No. That is the answer for this set of equations:

\begin{align*} \sqrt{x} + \sqrt{y} + \sqrt{z} &= 10, \\ x + y + z &= 38, \\ \sqrt{xyz} &= 30, \end{align*}

Guest May 25, 2021