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Determine the unique pair of real numbers (x,y) satisfying \((3x^2 - 12x + 16)(2y^2 + 6y + 9) = 18.\)

 May 16, 2020
 #1
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(x,y) = (4,-6).

 May 16, 2020
 #2
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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)

 May 16, 2020

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