RU-ALLRUSSIAN 1988 Problem 18

Find the minimum value of $\mathrm{xy / z + yz / x + zx / y}$ for positive reals $\mathrm{x}$ , $\mathrm{y}$ , $\mathrm{z}$ with $\mathrm{x}^{2} + \mathrm{y}^{2} + \mathrm{z}^{2} = 1$ .