Question

if (n +1)! =12 × (n -1)! find n

Answer 1

Hey there!♥️

_______________________________

(n+1)! = 12 × (n-1)!

(n+1)×n×(n-1)! = 12 × (n-1)!

(n+1)n = 12

n² + n = 12

n² + n - 12 = 0

n² + 3n - 4n - 12 = 0

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

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

n = 4 or -3

______________________

Hope it helps you♥️

Answer 2

$\huge\underline\mathfrak{Question\:\::-}$

If ( n + 1 ) ! = 12 × ( n - 1 )! find n.

$\huge\underline\mathfrak{answEr\:\::-}$

We have,

$\\ \qquad \tt \: (n + 1)! = 12 \times (n - 1)! \\ \\ \\ \implies \tt \: (n + 1) \times n \times (n - 1)! \\ \\ \\ \implies \tt \: 12 \times (n - 1)! \\ \\ \\ \implies \tt \: n(n + 1) = 12 \\ \\ \\ \implies \tt \: (n + 1)n = 4 \times 3 \qquad \sf \: (by \: comparing) \\ \\ \\ \implies \tt \pink{n = 3}$

Hence, the value of n will be 3.