Question: Complete the proof of Theorem 4.38(a) by showing that if the recurrence relation x n = ax n-1 + bx n-2 has distinct eigenvalues

Complete the proof of Theorem 4.38(a) by showing that if the recurrence relation x_n = ax_n-1 + bx_n-2 has distinct eigenvalues λ₁ ≠ λ₂, then the solution will be of the form
x_n = c₁λⁿ₁ + c₂λⁿ₂

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