RU-ALLRUSSIAN 1962 Problem 7

Given four positive real numbers a, b, c, d such that $\mathrm{abcd} = 1$ , prove that $\mathrm{a}^{2} + \mathrm{b}^{2} + \mathrm{c}^{2} + \mathrm{d}^{2} + \mathrm{ab} + \mathrm{ac} + \mathrm{ad} + \mathrm{bc} + \mathrm{bd} + \mathrm{cd} \geq 10$ .