Applyo - College Application Platform

CAT 2017 Slot 1 QA Question & Solution

AlgebraMedium

Question

If $a, b, c,$ and $d$ are integers such that $a+b+c+d=30$ then the minimum possible value of $(a - b)^{2} + (a - c)^{2} + (a - d)^{2}$  is

Solution

For the value of given expression to be minimum, the values of $a, b, c$ and $d$ should be as close as possible. 30/4 = 7.5. Since each one of these are integers so values must be 8, 8, 7, 7. On putting these values in the given expression, we get
 $(8 - 8)^{2} + (8 - 7)^{2} + (8 - 7)^{2}$
=> 1 + 1 = 2