My girlfriend's math teacher was offering this problem for extra credit:
(7x-2)^(1/3) + (7x+5)^(1/3) = 3
It was due today so it's too late to get extra credit for it, but it's been driving me and my friend completely insane because we are usually pretty proud of our math skills, but this one has us completely stumped. We know (thanks to an online math solver) that the solution is 3/7, but the point was to show steps. We tried using logs but that led us nowhere, and cubing the whole thing leads us to a dead end as well. Can someone at least give me a hint or something?
thanks