+0  
 
0
77
1
avatar

What is the minimum value of (x - 1)^2 + (x - 2)^2 + (x - 3)^2 + (x - 4)^2 + (x - 5)^2?

 Jun 14, 2020
 #1
avatar+8341 
0

Expanding them all and completing the square would be possible.

 

\(\)\((x - 1)^2 + (x - 2)^2 + (x - 3)^2 + (x - 4)^2 + (x - 5)^2 = 5x^2 - 30x + 55 = 5(x^2 - 6x + 11) = 5(x - 3)^2 + 10\)

 

Therefore if we substitute x = 3 into the expression, we get the minimum value.

 

The minimum value is 10.

 Jun 14, 2020

74 Online Users

avatar
avatar
avatar
avatar