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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.

This problem was taken from HSGS grade 10 selection test

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