If α and β are the greatest divisors of n n 2 - 1 and 2 n n 2 + 2 respectively for all n ∈ N , then α β =

Step-by-step solution

For n ∈ N ⇒ n = 1 ,   2 ,   3 … The values of n n 2 - 1 are n = 1 ⇒ 1 1 - 1 = 0 n = 2 ⇒ 2 4 - 1 = 2 3 = 6 n = 3 ⇒ 3 9 - 1 = 24 … The values of 2 n n 2 + 2 are, n = 1 ⇒ 2 1 + 2 = 6 n = 2 ⇒ 2 2 2 2 + 2 = 4 6 = 24 n = 3 ⇒ 2 3 3 2 + 2 = 6 11 = 66 … ∴ Greatest divisors of α and β are both 6 , ∴   α β = 6 6 = 36