Here is a statement that I came upon whilst studying Sobolev spaces, which I cannot quite fill in the gaps:
If $s>t>u$ then we can estimate: \begin{equation} (1 + |\xi|)^{2t} \leq \varepsilon (1 + |\xi|)^{2s} + C(\varepsilon)(1 + |\xi|)^{2u} \end{equation} for any $\varepsilon > 0$ (here $\xi \in \mathbb{R}^n$ and $C(\varepsilon)$ is a constant, dependent on $\varepsilon$).
How can I show this? Many thanks for hints!