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

Problem

Solution