When Towers Meet Radicals

Algebra Level 3

Find largest possible integer value of a such that

\(2+\cfrac{a}{2+\cfrac{a}{2+\cfrac{a}{2+...}}}>\sqrt{a\sqrt{a\sqrt{a\sqrt{a...}}}}\)

This is part of the set Fun With Problem-Solving.

Donglin Loo by donglin loo
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