This is another example of a substitution problem. Normally I would have just worked it out long hand, expanding thing and solving. That’s a lot of work and frankly kind of a foolish way to attack the problem looking at it now. Since I started looking for substitutions first – the problem collapses to simple in one substitution. Unfortunately its still fairly un-elegant – so I don’t think this is the solution they book is looking for.
The problem is stated as: “Solve: (6x+28)^1/3 – (6x-28)^1/3 = 2”