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

Revision as of 08:35, 14 February 2008

A function $f(x)$ is defined for all real numbers $x$ . For all non-zero values $x$ , we have

$2f\left(x\right) + f\left(\frac{1}{x}\right) = 5x + 4$

Let $S$ denote the sum of all of the values of $x$ for which $f(x) = 2004$ . Compute the integer nearest to $S$ .

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

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+==Problem==
-<math>3.</math> 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
+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>
 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==