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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
 #1
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One triple that wrks is (4,9,25).

 May 25, 2021
 #2
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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

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