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What is the minimum value of the expression x^2 + y^2 + 2x - 4y + 8 - 10y + 3y for real x and y?

 Jun 24, 2021
 #1
avatar+287 
+2

Completing the square on $x$ and $y$ independently to write the given expression as
$(x+a)^2+(y+b)^2+c$.   The answer is $c$.
 

 Jun 24, 2021
 #2
avatar+33551 
+1

Put into standard circle form :

 

(x +1)^2   +  (y-5.5)^2   = -8 +1+ 30.25              r = sqrt 23.25     center = -1, 5.5     

 

Minumum 'x'   will be     - 1 - sqrt 23.25

Minumum 'y' will be         5.5 - sqrt 23.5       (check my math)

 Jun 24, 2021

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