AoPS Wiki talk:Problem of the Day/July 13, 2011

Problem

AoPSWiki:Problem of the Day/July 13, 2011

Solution

We have $\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}=36$, so $x+\sqrt{x+\sqrt{x+\cdots}}=36^2=1296$, and $\sqrt{x+\sqrt{x+\cdots}}=1296-x$. However, we already know that the LHS is $36$, so we have $1296-x=36$, and $x=\boxed{1260}$.

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