Determine the unique pair of real numbers (x,y) satisfying \((3x^2 - 12x + 16)(2y^2 + 6y + 9) = 18.\)
(x,y) = (4,-6).
3x2 - 12x + 16 is a quadratic (parablola) that has a minimum of 4 (which occurs when x = 2 ).
2y2 + 6y + 9 is a quadratic that has a minimum of 4.5 (which occurs when y = -1.5).
Since 4 x 4.5 = 18, the pair of real numbers is (2, -1.5)
