# Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 3"

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− | + | ==Problem== | |

− | + | A function <math>f(x)</math> is defined for all real numbers <math>x</math>. For all non-zero values <math>x</math>, we have | |

<math>2f\left(x\right) + f\left(\frac{1}{x}\right) = 5x + 4</math> | <math>2f\left(x\right) + f\left(\frac{1}{x}\right) = 5x + 4</math> | ||

Let <math>S</math> denote the sum of all of the values of <math>x</math> for which <math>f(x) = 2004</math>. Compute the integer nearest to <math>S</math>. | Let <math>S</math> denote the sum of all of the values of <math>x</math> for which <math>f(x) = 2004</math>. Compute the integer nearest to <math>S</math>. | ||

+ | |||

+ | ==Solution== | ||

+ | {{solution}} | ||

+ | |||

+ | ==See also== |

## Revision as of 08:35, 14 February 2008

## Problem

A function is defined for all real numbers . For all non-zero values , we have

Let denote the sum of all of the values of for which . Compute the integer nearest to .

## Solution

*This problem needs a solution. If you have a solution for it, please help us out by adding it.*