\(xy=\dfrac{1}{2};yz=\dfrac{3}{5};xz=\dfrac{27}{10}\)
\(\Rightarrow xy.yz.xz=\dfrac{1}{2}.\dfrac{3}{5}.\dfrac{27}{10}\)
\(\Rightarrow\left(xyz\right)^2=\dfrac{81}{100}\)
\(\Rightarrow\left\{{}\begin{matrix}xyz=\dfrac{9}{10}\\xyz=\dfrac{-9}{10}\\xyz=\dfrac{9}{-10}\\xyz=\dfrac{-9}{-10}\end{matrix}\right.\)