2014 AMC 12B Problems/Problem 25
Problem
Find the sum of all the positive solutions of
$\textbf{(A)}\ \pi \qquad\textbf{(B)}\ 35\qquad\textbf{(C)}\ 1008\pi \qquad\textbf{(D)}}\ 1080 \pi \qquad\textbf{(E)}\ 1800\pi$ (Error compiling LaTeX. Unknown error_msg)
Solution
Rewrite as
. Now let
, and let
. We have
Notice that either
and
or
and
. For the first case, $x = 1