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If x, y, and z are positive with xy = 20(cube root 2), xz = 35 (cube root 2), and yz = 14(cube root 2), then what is xyz?

Guest Apr 5, 2018
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If x, y, and z are positive with xy = 20(cube root 2), xz = 35 (cube root 2), and yz = 14(cube root 2),

then what is xyz?

 

\(\begin{array}{|rcll|} \hline xy &=& 20\sqrt[3]{2} \\ xz &=& 35\sqrt[3]{2} \\ yz &=& 14\sqrt[3]{2} \\\\ xy\cdot xz\cdot yz &=& 20\sqrt[3]{2}\cdot 35\sqrt[3]{2} \cdot 14 \sqrt[3]{2} \\ x^2y^2z^2 &=& 20\cdot 35 \cdot 14 \cdot (\sqrt[3]{2} )^3 \\ (xyz)^2 &=& 20\cdot 35 \cdot 14 \cdot 2 \\ xyz &=& \sqrt{20\cdot 35 \cdot 14 \cdot 2} \\ xyz &=& \sqrt{19600} \\ \mathbf{xyz} &\mathbf{=} & \mathbf{140} \\ \hline \end{array}\)

 

laugh

heureka  Apr 5, 2018

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