# Are you smarter than a grade 9 student?

Algebra Level 5

$\large x^2(x^2+1)+y^2(y^2+1)$

Positive reals $x$ and $y$ satisfying the system of inequalities below.

$\begin{cases} x\leq y\leq 2 \\ 2x+y\geq 2xy\end{cases}$

Find the maximum value of the expression above.

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