Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 7, 2011"

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{{:AoPSWiki:Problem of the Day/June 7, 2011}}
 
{{:AoPSWiki:Problem of the Day/June 7, 2011}}
 
==Solution==
 
==Solution==
{{potd_solution}}
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<math>\sqrt{x+2}=x-18 \implies</math>
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<math>x+2=(x-18)^2=x^2-36x+324 \implies</math>
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<math>x^2-37x+322=0 \implies</math>
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<math>(x-23)(x-14)=0</math>.
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Clearly <math>x=14</math> is extraneous, so our answer is <math>x=\boxed{23}</math>.

Latest revision as of 14:58, 6 June 2011

Problem

AoPSWiki:Problem of the Day/June 7, 2011

Solution

$\sqrt{x+2}=x-18 \implies$ $x+2=(x-18)^2=x^2-36x+324 \implies$ $x^2-37x+322=0 \implies$ $(x-23)(x-14)=0$.

Clearly $x=14$ is extraneous, so our answer is $x=\boxed{23}$.

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