Question

If(n+2)c8:(n-2)p4=57:16 than find n

Answer 1

Answer:

n=19

Step-by-step explanation:

n+2C8 : n-2P4 = 57 : 16

⇒ {(n + 2 )! (n - 6)!} / {(n - 6)! (n - 2)! 8!} = 57/16

⇒ (n + 2) (n + 1) n(n - 1) = 143640

⇒ (n2 + n - 2) (n2 + n ) = 143640

⇒ (n2 + n )2 - 2(n2 + n) + 1 = 143641

⇒ (n2 + n - 1)2 = (379)2

[∵ n2 + n - 1 > 0]

⇒ n2 + n - 1 = 379

⇒ n2 + n - 380 = 0

⇒ (n + 20) (n - 19) = 0

∴n = 19 ( Since n is not negative)