IMO 1969 LL MON41

Given two numbers x0 and x1, let lpha and eta be coefficients

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IMO 1969 LL MON41

Origin: MON

Problem

Given two numbers x0 and x1, let \alpha and \beta be coefficients of the equation 1 −\alphay −\betay2 = 0. Under the given conditions, find an expression for the solution of the system xn+2 −\alphaxn+1 −\betaxn = 0, n = 0, 1, 2, . . . .