Nonlinear Equations of Degree 2

Algebra Level 5

{2x26xy+2y2+43x+43y=174,x2+y2+5x+5y=30 \begin{cases} 2x^2 - 6xy + 2y^2 + 43 x + 43 y &=& 174, \\ x^2 + y^2 + 5x + 5y &=& 30 \end{cases}

The real numbers xx and y y satisfy the nonlinear system of equations above.

Find the largest possible value of xy |xy|.

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