It is known that a and B are positive real numbers, and it is proved that (a + 1 / b) (B + 1 / b) ≥ 4

It is known that a and B are positive real numbers, and it is proved that (a + 1 / b) (B + 1 / b) ≥ 4

From the basic inequality
AB + 1 / AB ≥ 2 radical [AB * (1 / AB)] = 2 (if and only if AB = 1 / AB, i.e., ab = 1, take =)
Similarly, a / B + B / a ≥ 2 (if and only if a / b = B / A, i.e., a = B, take =)
（a+1/b)(b+1/b)
=ab+1/ab+a/b+b/a
≥ 4 (if and only if a = b = 1, take =)

If the positive real number a and B satisfy (A-1) (B-1) = 4, then the minimum value of a + B
Please write the process

(A-1)(B-1)=4
AB-A-B-1=4
AB=A+B+3
A + b > = AB under double root sign
AB = 6 or a + B

It is proved that for any real number a > b
There are always integer solutions for B ≤ K π + D ≤ a
Prove that this is a true proposition or a false proposition

In other words, it is proved that K π + D can approximate any real number x with any high degree of accuracy
K / D can approximate any real number x with any high degree of accuracy
(P, q) = D, then KP + DQ can be equal to any multiple of D
What is the relationship between the three?