Question

Find , if ( + 2)! = 90 × !.
Please its urgent

Answer 1

Your Question is Quite wrong It will be

(n+ 2)(n + 1) × n! = 90 × n!

Now

see the solution

Answer

We Have

(n + 2)(n + 1) × n! = 90 × n!

⇒  (n + 2)(n + 1) = 90

⇒  n² + 2n + n + 2 = 90

⇒  n² + 3n − 88 = 0

⇒  n² + 11n − 8n − 88 = 0

⇒  n(n + 11) − 8(n + 11) = 0

⇒  (n + 11)(n − 8) = 0

⇒  n = 8

[∴ n ≥ 0]

Hence ,

n = 8.