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What is the minimum value of the expression 2x^2 + y^2 + 8x - 24y + 62 for real x and y?

 Jul 29, 2022
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2x^2 + 8x + y^2 - 24y + 62    complete the square on x, y

 

2(x^2 + 4x + 4) + (y^2 - 24y + 144)  + 62 - 8 - 144

 

2 (x + 2)^2  + (y - 12)^2   -  90

 

The min of 90  occurs when x = -2  and  y = 12

 

 

cool cool cool

 Jul 29, 2022

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