Write x2 − 2x − 3 = 0 in the form (x − a)2 = b, where a and b are integers.

(a) (x − 4)2 = 3
(b) (x − 3)2 = 2
(c) (x − 2)2 = 1
(d)(x − 1)2 = 4

This is called the completing square method, and in order to carry out this method, we must follow certain steps. The first step is to ensure that the value of the coefficient of x^2 is 1, which it is. Next, we divide the second term, 2x in this case, by 2x. In this case, the quotient comes out to be 1. Now, we add the square of the quotient to both sides of the equation to obtain x^2 - 2x + 1 - 3 = 1. Next, we apply the completing square formula to obtain (x - 1)^2 - 3 = 1. Changing this into the required form, (x - 1)^2 = 4. The value of a is 1 and the value of b is 4. The answer is D.

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