Question

Find n, if:
(n + 3)! = 110 (n + 1)!

Answer 1

Answer:

n = 8 , n = -13

Step-by-step explanation:

In this question,

We need to find the value of n if

(n + 3)! = 110 (n + 1)!

According to the question

(n + 3)! = 110 (n + 1)!

(n + 3)(n + 2)(n + 1)! = 110(n + 1)!

Cancelling (n + 1)! from both sides

(n + 3)(n + 2) = 110

$n^{2}\ +\ 5n\ +\ 6\ =\ 110$

$n^{2}\ +\ 5n\ -\ 104\ =\ 0$

$n^{2}\ +\ 13n\ -\ 8n\ -\ 104\ =\ 0$

n(n + 13) - 8(n + 3) = 0

(n - 8)(n + 13) = 0

n - 8 = 0 ; n +13 = 0

n = 8      ; n = -13

We get the value of n as 8,-15