Let a, b, c, d be non-zero rational numbers, and let a = 1+√5 +√7-√√35. a) Can a¹ be written in the form a¹=e+f√5 + g√7+h√35 for rational numbers e, f, g, h? Fully justify your answer. b) You are told that a is a root of the polynomial p(x) = x³ +p₁2¹+P3x³ + p2r² + p1x + po with rational coefficients. Find three further roots. c) Find values of Po, P1, P2, P3, P4 which make this true.