Final answer:
The correct answer is option A. Among the options given, option A (5√x = -2) is the one that has an extraneous solution, as the process of squaring both sides to eliminate the square root may introduce a solution that is not valid for the original equation.
Step-by-step explanation:
The question asks which equation has an extraneous solution. An extraneous solution is a solution that emerges from the solving process of the equation but isn't a valid solution to the original equation.
Looking at the options provided, the only one that can have an extraneous solution is option A (5√x = -2). This is because when we square both sides to eliminate the square root, additional solutions may be introduced that are not solutions to the original equation. For example, squaring both sides would give us (5√x)2 = (-2)2, simplifying to 25x = 4. However, the original equation does not have a real solution since the square root of x must be a non-negative number, and thus cannot equal -2.
Options B, C, and D do not contain any operations that would introduce extraneous solutions when solved. Therefore, the correct option that contains an extraneous solution is option A (5√x = -2).