Think Positive

Algebra Level 3

$\large{\begin{cases} a + 2b -12 > 0 \\ 3a - b -17 > 0 \\ 80 - 9a -4b > 0 \end{cases}}$

Given that $$a$$ and $$b$$ are integers satisfying system of the inequalities above, compute $$a^2 + b^2$$.

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