Answer: C

Expression= (x−a)^2+(x−b)^2 = 2x^2 - 2ax -2bx +a^2 + b^2

For extreme values of expression, d/dx(expression) =0

Differentiating,

d/dx(expression) = 4x -2a -2b = 0

or, 4x= 2a+2b = 4a+8 [putting values of b=a+4]

Therefore, x= a+2

It can be ascertained that this extreme value is minimum as d^2/dx^2(expression) = 4 (positive)

Note: Differentiation is not tested on the GMAT, but following little information helps

1. d/dx(constant) = 0

2. d/dx(x^n) = n * x^(n-1)

3. d/dx(c*x) = c ; where c = constant

4. Expression has extreme values at d/dx(expression)=0

; d2/dx^2(expression) = positive signifies minimum value

; d2/dx^2(expression) = negative signifies maximum value

_________________

__________________________________

Kindly press "+1 Kudos" if the post helped