solutia n ∈ N conditie n ≥ 2
n! / ( n -3) ! · ( n - n +3)! - n! / ( n -2 ) ! = 3n
( n -3) ! ·( n -2) ·( n -1) · n / ( n -3) ! · 3! - ( n -2) ! · ( n -1) · n / ( n -2 ) ! = 3n
( n -2) · ( n -1) · n / 6 - ( n -1) · n - 3n = 0
n [ ( n -2) ·( n -1) - 6 ( n -1) - 18 ] = 0
n =0 fals
n² - 2n - n + 2 -6n + 6 - 18 =0
n² - 9n - 10 =0 Δ = 81 + 40 = 121
n = ( 9 -11 ) / 2 = - 1 fals , n∈ N
n = ( 9 + 11 ) /2 = 20 / 2 =10 solutie
