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2. Recall that the Fibonacci sequence F(n) is defined by the recurrence relation F(0) 0, F(1), and F(n) Fn -1) + F(n-2) for n1. a. Show that if a (1+V5)/2 and b-(1-V5)/2 then a2-a-1-b2-b-1 0 Conclude that a2 a 1 and that b2b1 b. Prove via induction that a"-b a -b F(n)