Difference between revisions of "AoPS Wiki talk:Problem of the Day/July 12, 2011"

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{{:AoPSWiki:Problem of the Day/July 12, 2011}}
 
{{:AoPSWiki:Problem of the Day/July 12, 2011}}
 
==Solution==
 
==Solution==
{{potd_solution}}
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Note that
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<cmath>\sqrt{1+\sqrt{1+\sqrt{1}}}=\sqrt{1+\sqrt{2}}</cmath>
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Thus:
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<cmath>(\sqrt{1+\sqrt{2}})^4=(1+\sqrt{2})^2=\boxed{3+2\sqrt{2}}</cmath>
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and we are done.

Latest revision as of 22:31, 11 July 2011

Problem

AoPSWiki:Problem of the Day/July 12, 2011

Solution

Note that \[\sqrt{1+\sqrt{1+\sqrt{1}}}=\sqrt{1+\sqrt{2}}\] Thus: \[(\sqrt{1+\sqrt{2}})^4=(1+\sqrt{2})^2=\boxed{3+2\sqrt{2}}\] and we are done.

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