Let x n , n 0, be a sequence of nonzero real numbers such that x 2 n x n 1 X n 1 1 for n 1, 2, 3, Prove there exists a real number a such that X n 1 ax n x n 1 for all n 1

Question: Let {x n }, n 0, be a sequence of nonzero real numbers such that x 2 n - x n -1 X n+1

Let {x_n}, n ≥ 0, be a sequence of nonzero real numbers
such that x²_n - x_n_-1 X_n+1= 1 for n = 1, 2, 3, . . . . Prove
there exists a real number a such that X_n+1 = ax_n - x_n-1 for all n ≥ 1.

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