if n is a positive integer such that n! / ( n - 2 )! = 342, find n. Select
A) 17	B) 18	C) 19	D) 20	E) 21
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">342 + (1/4)</gadget>
<output>1_369/4 = around 342.25</output>

<gadget id="calculator">(1_369/4) ** (1/2)</gadget>
<output>37/2 = around 18.5</output>

<result>C</result>
if n is a positive integer such that n! / ( n - 2 )! = 342, find n.
sqrt(add(342, divide(const_1, const_4)))
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