The number of elements in the set n ∈ ℤ : n 2 - 10 n + 19 < 6 is _______ .

Step-by-step solution

Given, n 2 - 10 n + 19 < 6 Now we know that, x < a ⇒ - a < x < a Now using above formula we get, ⇒ - 6 < n 2 - 10 n + 19 < 6 ⇒ n 2 - 10 n + 25 > 0 and n 2 - 10 n + 13 < 0 ⇒ n - 5 2 > 0 and n - 5 - 2 3 n - 5 + 2 3 < 0 ⇒ n ∈ ℤ - 5 and n ∈ 2 ,   3 ,   4 ,   5 ,   6 ,   7 ,   8 Hence, n = 2 ,   3 ,   4 ,   6 ,   7 ,   8