I am still learning how to use the forum features so read carefully as I was unable to do the math formulas

I dont know if this is a GMAT question.. but here is what is how I would approach this by logic.

1. Note that in this expression you have a spread of 4 (the difference between A and B) to be distributed in 2 parts.

2. The distribution should be such that sum of squares is minimized. The minimum would be 2 (square) + 2 (square) = 8

Hence, X = A+2

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Alternate approachLet X = A+K, where K is a constant

Expression: \((A+K-A)^2\) + \((A+K-A-4)^2\)

Simplifying: \(k^2\) + \((k-4)^2\)

This is minimum for k = 2

I hope this helps.

-Rajat

Alternate questionWhat would be the value of X for (X - A)^2

- (X - B)^2 to be smallest? What is the smallest value.

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