Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 4, 2011"

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==Answer==
 
==Answer==
 
<math>\boxed{\frac{3}{10}}</math> {{toadd}}
 
<math>\boxed{\frac{3}{10}}</math> {{toadd}}
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== Solution ==
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Since <math>0<x<1</math>, <math>\lfloor x\rfloor=0</math> and <math>\lceiling x\rceiling=1</math>, so the equation becomes <math>10x^2+\frac{0}{1}=\frac{9}{10}</math> <cmath>10x^2=\frac{9}{10}</cmath> <cmath>x^2=\frac{9}{100}</cmath> <cmath>x=\boxed{\frac{3}{10}}</cmath>

Revision as of 08:41, 4 June 2011

Problem

AoPSWiki:Problem of the Day/June 4, 2011

Answer

$\boxed{\frac{3}{10}}$


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Solution

Since $0<x<1$, $\lfloor x\rfloor=0$ and $\lceiling x\rceiling=1$ (Error compiling LaTeX. Unknown error_msg), so the equation becomes $10x^2+\frac{0}{1}=\frac{9}{10}$ \[10x^2=\frac{9}{10}\] \[x^2=\frac{9}{100}\] \[x=\boxed{\frac{3}{10}}\]