VMO 1964 Problem 4

Define the sequence of positive integers $f_n$ by $f_0 = 1, f_1 = 1, f_{n+2} = f_{n+1} + f_n$ . Show that $f_n =\frac{ (a^{n+1} - b^{n+1})}{\sqrt5}$ , where $a, b$ are real numbers such that $a + b = 1, ab = -1$ and $a > b$ .