Problem: if n is a positive integer such that n ! / ( n - 2 ) ! = 342 , find n .
Rationale: we write n ! = n * ( n - 1 ) ( n - 2 ! ) therefore n ! / ( n - 2 ) ! = n ( n - 1 ) * ( n - 2 ) ! / ( n - 2 ) ! = n ( n - 1 ) . - - > n ( n - 1 ) = 342 - - > n ^ 2 - n - 342 = 0 - - > n ^ 2 - 19 n + 18 n - 342 = 0 - - > n ( n - 19 ) + 18 ( n - 19 ) = 0 - - > ( n - 19 ) ( n + 18 ) = 0 therefore n - 19 = 0 ; n + 18 = 0 ; ( i . e ) n = 19 ; n = - 18 we want positive integer . so , n = 19 . answer : c
annotated_formula: sqrt(add(342, divide(const_1, const_4)))