(a) For a = (1 + 5)/2 and = (1 - 5)/2, verify that a2 -...

(a) For a = (1 + √5)/2 and β = (1 - √5)/2, verify that a2 - a-2 = a - β = β-2 -β2.
(b) Prove that F2n = F2n+l - F2n-1, n ≥ 1.
(c) For n ≥ 1, let T be an isosceles trapezoid with bases of length Fn-1 and Fn+1, and sides of length Fn. Prove that the area of T is (√3/4)F2n.