On one hand, (notice the very last statement)

...

On the other hand,

[math]x=\sqrt[5]{2+5\sqrt[5]{2+5\sqrt[5]{2+...}}}[/math]

solves that polynomial.

What's wrong?

Edited Tuesday at 03:30 PM2 days by Genady

5 hours ago, Genady said:

What's wrong?

I don't think a solution in terms of radicals includes infinitely nested radicals.

However, it is my (possibly incorrect) understanding that all quintic equations can be solved in terms of the Bring radical (an ultraradical).

Edited Tuesday at 09:19 PM1 day by KJW

14 minutes ago, KJW said:

I don't think a solution in terms of radicals includes infinitely nested radicals.

You are correct. It includes only a finite number of radicals.

Edited Tuesday at 09:38 PM1 day by Genady