Let a, b ∈ R.
a) Prove that if a > 2 and b = 1 + √a - 1, then 2 < b < a.
b) Prove that if 2 < a < 3 and = 2 + √a - 2, then 0 < a < b.
c) Prove that if 0 < a < 1 and b = 1 - √l - a, then 0 < b < a.
d) Prove that if 3 < a < 5 and b = 2 + √a - 2, then 3 < b < a.