MathNet 1982 — Part 01 Question 19

$\mathbf{x}$ 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 $2^{\mathrm{a}} + 2^{\mathrm{b}} \geq 2^{1 + \mathrm{c}}$.