Beautiful trick. There's exactly one point where the problem is introduced, and it's one of the subtler ways you can go wrong with solving an equation algebraically... Hint: Consider the problem, step-by-step, in the complex plane. Every quadratic has either two solutions or is a perfect square. This one's not a perfect square. At one point, we turn it into a cubic - which necessarily has either three or two solutions. This one has three. Where'd the extra solution come from?

Bizarrely, I did - despite being born in 1987. Skiffle's not really my thing, either. But I took this class on the Beatles in college, and well, you can't AVOID skiffle, given how heavily it influenced them.

As for Connecticut Yankee - I can't second this one strongly enough. Sci-fi & fantasy, with some wonderful play with the story. It'd probably help if they knew at least a bit of the King Arthur myths first, though.