It is known that the domain of F (x) = 1 / √ x * x + ax + B is a, and the domain of G (x) = √ k * x * x + 4x + K + 3 is B If (CRA) ∩ B = B, (CRA) ∪ B = {x | x is greater than or equal to 2 and X is less than or equal to 3}, find the value of a and B and the value range of K Note: the value range of K needs detailed process

It is known that the domain of F (x) = 1 / √ x * x + ax + B is a, and the domain of G (x) = √ k * x * x + 4x + K + 3 is B If (CRA) ∩ B = B, (CRA) ∪ B = {x | x is greater than or equal to 2 and X is less than or equal to 3}, find the value of a and B and the value range of K Note: the value range of K needs detailed process

analysis:
(1) The domain a of (x) is obtained from the solution of X * x + ax + b > 0, so it is in the form of XN
∩ (CRA) ∩ B = B, ∪ B is a subset of (CRA). ∪ B = (CRA) ∪ B = {x | x is greater than or equal to 2 and X is less than or equal to 3}, ∩ a = {x | X3}. ∩ 2 and 3 are two solutions of the equation x * x + ax + B = 0
(2) From (1), we know that B is a subset of (CRA), and the domain B of G (x) is obtained from the solution of K * x * x + 4x + K + 3 ≥ 0, so it is m ≤ x ≤ n. let H (x) = k * x * x + 4x + K + 3, and its image symmetry axis is - 2 / K