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For all real numbers x, find the minimum value of (x + 12)^2 - (x + 7)^2 + (x + 13)^2 - (x - 14)^2 + (x - 18)^2 

 Jun 19, 2024
 #1
avatar+129733 
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Simplifying we get

 

x^2  - 28x + 392

 

The  minimum  value occurs at  x =   28 / [ 2 * 1 ] =  14

 

And  the minimum value is

 

(14)^2 -28(14) + 392   =  196

 

cool cool cool

 Jun 19, 2024
edited by CPhill  Jun 19, 2024

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