We have positive real numbers a and b such that a + b = 1. To find the set of all possible values of 1/a + 1/b, we can use the AM-HM inequality:

    (a + b)/2≥2/(1/a + 1/b)

From this we can simplify:

    1/a + 1/b≥4/(a + b) = 4

The minimum possible value is 4, which is achieved when a = b = 1/2. 

However, as a approaches 0 and b approaches 1, 1/a + 1/b becomes arbitrarily large. Therefore, the set of all possible values of 1/a + 1/b is [4,∞).
Siano a e b numeri reali positivi tali che a + b = 1. Trova l'insieme di tutti i possibili valori di 1/a + 1/b.