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x_k+x_{k+1}=x^2_{k+2} , n x n system

Source: Bosnia and Herzegovina EGMO TST 2019 p1

October 7, 2022
algebrasystem of equations

Problem Statement

Let x1,x2,...,xnx_1,x_2, ..., x_n be non-negative real numbers. Solve the system of equations: xk+xk+1=xk+22  ,   (k=1,2,...,n),x_k+x_{k+1}=x^2_{k+2}\,\,,\,\,\, (k =1,2,...,n), where xn+1=x1x_{n+1} = x_1, xn+2=x2x_{n+2} = x_2.
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