# For all $x,y\geq 0$ show that $\frac{x^2+y^2}{4}\leq e^{x+y-2}$ [duplicate]

How do I show that for all $x,y\geq 0$, $\frac{x^2+y^2}{4}\leq e^{x+y-2}$? Tried using the mean value theorem but couldn't figure out how to use it properly.

## marked as duplicate by Claude Leibovici, vrugtehagel, Mark, pre-kidney, JonMark PerryMar 26 '17 at 8:19

• @user8795 the question is asking for $e^{x+y-2}$, so the series would contain positive and negative terms, so that method does not work directly. – adfriedman Mar 26 '17 at 7:53