AoPS Wiki talk:Problem of the Day/June 4, 2011

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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. ! Undefined control sequence.), the equation becomes $10x^2+\frac{0}{1}=\frac{9}{10}$ \[10x^2=\frac{9}{10}\] \[x^2=\frac{9}{100}\] \[x=\boxed{\frac{3}{10}}\]

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