Difference between revisions of "AoPS Wiki talk:Problem of the Day/July 13, 2011"
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==Solution== | ==Solution== | ||
− | {{ | + | We have <math> \sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}=36 </math>, so <math> x+\sqrt{x+\sqrt{x+\cdots}}=36^2=1296 </math>, and <math> \sqrt{x+\sqrt{x+\cdots}}=1296-x </math>. However, we already know that the [[LHS]] is <math> 36 </math>, so we have <math> 1296-x=36 </math>, and <math> x=\boxed{1260} </math>. |
Latest revision as of 12:33, 13 July 2011
Problem
AoPSWiki:Problem of the Day/July 13, 2011
Solution
We have , so , and . However, we already know that the LHS is , so we have , and .