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If $\mathrm{x}_{\mathrm{i}}>0, \mathrm{y}_{\mathrm{i}}>0(\mathrm{i}=1,2,3, \ldots \ldots \mathrm{n})$ are the values of two variable $X$ and Y with geometric mean Pand Q respectively, then the geometric mean of $\frac{\mathrm{X}}{\mathrm{Y}}$ is
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antilog $\left(\frac{\mathrm{P}}{\mathrm{Q}}\right)$
$\left(x_{1} x_{2} \ldots \ldots \ldots x_{n}\right)^{1 / n}=\mathrm{P}$
$\left(y_{1} y_{2} \ldots \ldots . y_{n}\right)^{1 / n}=\mathrm{Q}$
$\left(\frac{x_{1} \cdot x_{2} \ldots \ldots \ldots \ldots x_{n}}{y_{1} \cdot y_{2} \ldots \ldots \ldots . y_{n}}\right)^{1 / n}=\frac{\left(x_{1} \cdot x_{2} \ldots \ldots \ldots \ldots x_{n}\right)^{1 / n}}{\left(y_{1} y_{2} \ldots \ldots \ldots . y_{n}\right)^{1 / n}}=\frac{\mathrm{P}}{\mathrm{Q}}$
$\left(y_{1} y_{2} \ldots \ldots . y_{n}\right)^{1 / n}=\mathrm{Q}$
$\left(\frac{x_{1} \cdot x_{2} \ldots \ldots \ldots \ldots x_{n}}{y_{1} \cdot y_{2} \ldots \ldots \ldots . y_{n}}\right)^{1 / n}=\frac{\left(x_{1} \cdot x_{2} \ldots \ldots \ldots \ldots x_{n}\right)^{1 / n}}{\left(y_{1} y_{2} \ldots \ldots \ldots . y_{n}\right)^{1 / n}}=\frac{\mathrm{P}}{\mathrm{Q}}$
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