OG详解-OG8 数学1 Q24

Choice C is correct. Subtracting the expression (x-29) from both sides of the given equation yields 0 = (x-a)(x-29)-(x-29), which can be rewritten as 0 = (x-a)(x-29)+(-1)(x-29). Since the two terms on the right-hand side of this equation have a common factor of (x-29), it can be rewritten as 0 = (x-29)(x-a+(-1)), or 0 = (x-29)(x-a-1). Since x-a-1 is equivalent to x-(a+1), the equation 0 = (x-29)(x-a-1) can be rewritten as 0 = (x-29)(x-(a+1)). By the zero product property, it follows that x-29 = 0 or x-(a+1)= 0. Adding 29 to both sides of the equation x-29 = 0 yields x = 29. Adding a +1to both sides of the equation x-(a+1)= 0 yields x = a+1. Therefore, the two solutions to the given equation are 29 and a +1. Thus, only a +1and 29,   not a, are solutions to the given equation.
Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.