If x^2 + a = b and x is an integer, what could be the value of b-a

From the question data, x is an integer; therefore, \(x^2 \) is the square of an integer and the square of an integer is always a Perfect square.

\(x^2\) + a = b can be written as b –a = \(x^2\).

We do this rearrangement since we need the value of the expression, b-a. This is a basic hygiene rule – keep the required variable / expression on one side of the equation and take all other components on to the other side.

From the re-arranged equation, we can see that b-a = Perfect square.

The only perfect square in the options is 4. Note that this is a could-be question, so we are only looking for a possible value for b-a.
4 is definitely a possible value for b-a.

The correct answer option is B.

Hope that helps!
Aravind B T