Can anyone point me to any reference on the following inequality: Let $c>0, a,b \in \Bbb{R}$ $ \|a+b\|^2 \leq (1+c)\|a\|^2+(1+{\textstyle\frac{1}{c}})\|b\|^2 $
I'm not even sure if "Bohr's Inequality" is this inequality's name, since I can't find it anywhere in the internet.
I'm having a bad day and I got stuck in this one, apparently. Any suggestions or hints on how to prove it will be appreciated.