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 type the two equations here (or re-upload them)? That will let me pick the exact option.

In general, though, the key fact is:

- Raising both sides to an odd power (e.g. cubing) is a one-to-one operation on the reals, so it does not introduce extraneous solutions.
- Raising both sides to an even power (e.g. squaring) can introduce extraneous solutions (sign flips), so you must check any candidate solutions in the original equation.

So the correct choice is the one that says “both equations have the same potential solutions, but the equation that involves the square root might have extraneous solutions.” If equation A has the square root, pick option 3; if equation B has the square root, pick option 4. Options 1 and 2 are not generally correct.