I don't really know how to start proving this question.
Let $\xi$ and $\eta$ be random variables with $E(\xi)=E(\eta)=0$, $V(\xi)=V(\eta)=1$, and correlation coefficient $r$. Show that $$ E(\max(\xi^2,\eta^2))\leq1+\sqrt{1-r^2}. $$ Does anyone here have any idea for starting this question please?