Given $R$ is a ring, and $b$ is some positive integer such that $x + x^{2b + 1} = x^{2b} + x^{10b + 1}$ for all $x \in R$, prove that $R$ is Boolean, i.e. $x =x^2$ for all $x$ in $R$.
I am not sure where to begin with the problem, and what avenue of approach I should take such that my methodology is inclusive to all $x$ in R. Would it be feasible to convert this problem into matrix form, and then prove $A = A^2$?