Let a > 0 ,   a ≠ 1 . Then, the set S of all positive real numbers b satisfying 1 + a 2 1 + b 2 = 4 a b is

Step-by-step solution

Given relation 1 + a 2 1 + b 2 = 4 a b ⇒   a 2 + b 2 - 2 a b = 2 a b - 1 - a 2 b 2 ⇒   a - b 2 = - 1 - a b 2 ∵   a > 0 ,   a ≠ 1 and b is a positive real number ∴   a - b 2 ≠ 0 ≠ - 1 - a b 2 , because a - b 2 and 1 - a b 2 are non-negative real numbers. ∴ Set S is an empty set.