RU-ALLRUSSIAN 1982 Problem 15

$\mathbf{x}$ is a positive integer. Put $\mathbf{a} = \mathbf{x}^{1 / 12}$ , $\mathbf{b} = \mathbf{x}^{1 / 4}$ , $\mathbf{c} = \mathbf{x}^{1 / 6}$ . Show that $2^{\mathrm{a}} + 2^{\mathrm{b}} \geq 2^{1 + \mathrm{c}}$ .