Difference between revisions of "2005 AIME II Problems/Problem 7"

 
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== Problem ==
 
== Problem ==
In quadrilateral <math>ABCD</math>, <math>BC=8</math>, <math>CD=12</math>, <math>AD=10</math> and <math>m\angle A=m\angle B=60\circ</math>. Given that <math>AB=p+\sqrt{q}</math>, where ''p'' and ''q'' are positive integers, find <math>p+q</math>.
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Let <math> x=\frac{4}{(\sqrt{5}+1)(\sqrt[4]{5}+1)(\sqrt[8]{5}+1)(\sqrt[16]{5}+1)}. </math> Find <math> (x+1)^{48}. </math>
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== Solution ==
 
== Solution ==
 
== See Also ==
 
== See Also ==
 
*[[2005 AIME II Problems]]
 
*[[2005 AIME II Problems]]

Revision as of 22:23, 8 July 2006

Problem

Let $x=\frac{4}{(\sqrt{5}+1)(\sqrt[4]{5}+1)(\sqrt[8]{5}+1)(\sqrt[16]{5}+1)}.$ Find $(x+1)^{48}.$

Solution

See Also

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