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Algebra Level 5

x2(x2+1)+y2(y2+1)\large x^2(x^2+1)+y^2(y^2+1)

Positive reals xx and yy satisfying the system of inequalities below.

{xy22x+y2xy\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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