Question

Which comparison of the two equations is accurate?

Answer 1

9514 1404 393

Answer:

  (c) Both equations have the same potential solutions, but equation A might have extraneous solutions.

Step-by-step explanation:

The general approach to solving an equation like either of these is to raise both sides of the equation to a power that will remove the radical. In both cases, the result is a quadratic with roots of x=-4 and x=2.

Of these two potential solutions, x = -4 is an extraneous solution for equation A. Both values of x are solutions for equation B. An appropriate description is ...

  Both equations have the same potential solutions, but equation A might have extraneous solutions.

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Additional comment

The attached graph shows the equations cast into the form f(x) = 0, so x-intercepts are the solutions to the equation. The radical versions of the equations have only x-intercepts that are actual solutions. The version with the radicals removed is a parabola with two solutions (orange). Only one of those matches the solution to equation A (red). Both match the solutions of equation B (purple).