2. Recall that the Fibonacci sequence F(n) is defined by the recurrence relation F(0) = 0, F(1) = 1, and F(n) = F(n 1) + F(n 2) for n > 1.

a. Show that if a = (1+ 5)/2 and b = (1 5)/2 then a 2a1 = b 2b1 = 0. Conclude that a 2 = a + 1 and that b 2 = b + 1.

b. Prove via induction that F(n) = a n b n a b

please neat and show work.