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How many positive xxx satisfy
x+x+x+…+⋯x⏟n square roots=1\Large \sqrt{x} + \sqrt{\sqrt{x}} + \sqrt{\sqrt{\sqrt{x}}} + \ldots + \underbrace{\sqrt{\sqrt{\sqrt{\cdots\sqrt{x}}}}}_{n \text{ square roots}}=1x+x+x+…+n square roots⋯x=1
for a given positive integer n?n?n?
Bonus: What sorts of bounds can you put on these solution(s) in terms of n?n?n?
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