Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

(start of talk page)
 
(→‎Solution)
 
Line 2: Line 2:
 
{{:AoPSWiki:Problem of the Day/June 7, 2011}}
 
{{:AoPSWiki:Problem of the Day/June 7, 2011}}
 
==Solution==
 
==Solution==
−
{{potd_solution}}
+
<math>\sqrt{x+2}=x-18 \implies</math>
 +
<math>x+2=(x-18)^2=x^2-36x+324 \implies</math>
 +
<math>x^2-37x+322=0 \implies</math>
 +
<math>(x-23)(x-14)=0</math>.
 +
 
 +
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 $x=\boxed{23}$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki_talk:Problem_of_the_Day/June_7,_2011&oldid=39295"