It is known that f (x) = x & sup2; - (K-2) x + K & sup2; + 3K + 5 has two zeros if the two zeros of the function are α and β, Find the value range of α & # 178; + β & # 178

It is known that f (x) = x & sup2; - (K-2) x + K & sup2; + 3K + 5 has two zeros if the two zeros of the function are α and β, Find the value range of α & # 178; + β & # 178

∵ 5 has two zeros
∴△=b^2-4ac>0
(k-2)^2-4*(k^2+3k+5)>0
k^2-4k+4-4k^2-12k-20>0
3k^2+16k+16

Given the function f (x) = (x-1) ^ 2; G (x) = K (x-1), one of the zeros of the function f (x) - G (x) is 5, the sequence an satisfies A1 = K / 2 and (a (n + 1) - an) g (an) + F (an) = 0
(1) To prove the general formula of sequence an-a (n-1)
(2) Finding the sum of the first n terms of an

From the known, f (x) - G (x) = (x-1) ^ 2; G (x) = K (x-1), substituting x = 5, we can see that the result of the above formula is 0, the solution is k = 4, then A1 = 2
We can get (an-1) (4a (n (n (n + 1) (4a (n (n + 1) - 3A (n (n + 1) - 3an-1) = 0. Because an can't be equal to 0, then 4a (n + 1) - 3an-1 = 0, and there are 4 (a (n + N + 1) - 1) - 1) = 3 (an-1) in the move term, there are 4 (a (n + N + 1) - 4 (a (n + N + 1) - 1) = 3 (an-1), let BN = n = an, then there are 4B (n (n + 1) = 4bn, and B1 = A1, and B1 = A1-1 = 1, and B1 = A1 = 1. We know that BN is an arithmetic sequence, and its general term is BN = (BN = (3 / 4) ^ (3 / 4) ^ (n (n-1) in this paper, and then we can be an = 1 + (3 / 4) / (3 / 4) ^ (3 / 4) ^ (3 / 4) ^1)
The first n terms of an and Sn = (1 + 1 + 1 +...) +1)+(0+3/4+…… +(3 / 4) ^ (n-1)) (the front is the addition of N ones, followed by an equal ratio sequence) = n + 4 * (3 / 4) ^ n

Given the function f (x) = LNX + ax + 1 (a ∈ R). (1) when a = 92, if the function g (x) = f (x) - K has only one zero point, find the value range of real number k; (2) when a = 2, try to compare the size of F (x) and 1

(1) When a = 92, G (x) = LNX + 92 (x + 1) - K, G '(x) = 1x-92 (x + 1) 2 = 2x2 − 5x + 22x (x + 1) 2 = 0, the root of the equation is: X1 = 2, X2 = 12 & nbsp; from the definition domain of G (x), we can know that x > 0; ∵ when 0 < x < 12 & nbsp; G' (x) > 0, G (x) increasing function, when 12 < x < 2 & nbsp