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The real numbers x and y satisfy the nonlinear system of equations

{2x^2 − 6xy + 2y^2+ 43x + 43y = 174 x^2 + y^2 + 5x + 5y = 30.
Find the largest possible value of |xy|.

1 answer

2x^2 − 6xy + 2y^2+ 43x + 43y = 174
x^2 + y^2 + 5x + 5y = 30

Intersect at (-2,4),(4,-2),(1,3),(3,1)

Max |xy| is thus 8
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