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What is the minimum value of z if z=x^2+2y^2+6x-4y+22?

WhichWitchIsWhich  Oct 24, 2017
 #1
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z = x^2+2y^2+6x-4y+22   complete the square on x and y

 

[x^2 + 6x + 9]  +  2 [ y^2 - 2y + 1]  +  22   =  z + 11

 

(x +3)^2   + 2(y -1)^2   =   z - 11

 

This will be minimized when  the right side = 0    ⇒   z = 11

 

 

 

cool cool cool

CPhill  Oct 24, 2017

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