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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|.

  • math -

    This has been posted many times, and answered more than once by different teachers.

    The solution to the system of algebraic equations are:
    (3,1),(1,3),(-2,4),(4,-2).
    The maximum value of |xy| is therefore 8.

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