Question

Which comparison of the two equations is accurate?

Equation A: mc021-1.jpg
Equation B: mc021-2.jpg
Both equations have different solutions because the square root of a number is not the same as the cube root of a number.
Both equations result in different equations after eliminating the radicals, so they have the different solutions.
Both equations have the same potential solutions, but equation A might have extraneous solutions.
Both equations have the same potential solutions, but equation B might have extraneous solutions.

Answer 1

I can't see the images — could you paste the two equations as text or re-upload the pictures? That said, here’s how to decide and the likely correct choice:

- If Equation A contains a square root (√) and Equation B contains a cube root (∛), then the correct choice is:
"Both equations have the same potential solutions, but equation A might have extraneous solutions." (option 3.)

Reason: raising both sides to the 2nd power (to remove a square root) can produce extraneous roots because +a and −a both square to a^2. Raising both sides to the 3rd power (to remove a cube root) does not produce extraneous roots in that way because cubing is one-to-one over the reals, so any solution remains valid. In all cases you should isolate the radical, raise to the appropriate power, solve, and then check each candidate in the original equation to discard extraneous roots.

If the roles of square/cube roots are reversed (A is cube root and B is square root), choose option 4 instead. If both use even-index radicals, both can produce extraneous roots. If you post the actual equations I’ll give the definite answer and show the checks.