Question

the value of n n!÷(n-2)!=12,2<n​

Answer 1

Answer:

Required value of n is 4.

Step-by-step explanation:

Given,

n! / ( n - 2 )! = 12

$\implies \dfrac{n!}{(n-2)!}=12\\\\\\\implies\dfrac{n\times (n-1) \times (n-2)!}{(n-2)!}=12\\\\\\\implies n(n-1) =12$

= > n^2 - n = 12

= > n^2 - n - 12 = 0

= > n^2 - ( 4 - 3 )n - 12 = 0

= > n^2 - 4n + 3n - 12 = 0

= > n( n - 4 ) + 3( n - 4 ) = 0

= > ( n - 4 )( n + 3 ) = 0

= > n = 4 or - 3

Given, 2 < n{ n is greater than 2 }, so value of n can't be - 3.

Thus required value of n is 4.