Incorrect use of solve

It's correct use, but potentially incorrect results, of solve.

Apparently the exponent 1/3 is problematic. When given "(2*x+1)^(1/3)-(x^3-1)/2, solve x",

this is what WolframAlpha makes of it:

Note that:

and

each give you all 9 roots, but:

Gives 7 roots, and 6 duplicates. maybe if you add ", all" to the solve command it comes up with more.

Finally, check if -1 is a solution:

Apparently not. This is the wonder world of the exponent function when it's argument is (potentially) complex.

Success!

Luc