Radical Radicals
Algebra
Level
4
How many positive \(x\) satisfy
\[\Large \sqrt{x} + \sqrt{\sqrt{x}} + \sqrt{\sqrt{\sqrt{x}}} + \ldots + \underbrace{\sqrt{\sqrt{\sqrt{\cdots\sqrt{x}}}}}_{n \text{ square roots}}=1\]
for a given positive integer \(n?\)
Bonus: What sorts of bounds can you put on these solution(s) in terms of \(n?\)
by
Eli Ross