Find the number of real solutions to \[(x^{2006} + 1)(x^{2004} + x^{2002} + x^{2000} + \dots + x^2 + 1) = 2006x^{2005}.\]
By Descartes Rule of Signs, there are three real soutions.
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"by the some rule, this is the answer"
do not enter the answer
