If (n + 1)! = 90 [(n - 1)!], find n. - Vidyadip

Question

If (n + 1)! = 90 [(n - 1)!], find n.

✓

Answer

We have,

(n + 1)! = 90 [(n - 1)!]

⇒ (n + 1)! × n × (n - 1)! = 90 [(n - 1)!]

⇒ n (n + 1) = 90

⇒ n² + 10n - 9n - 90 = 0

⇒ n² (n + 10) - 9 (n + 10) = 0

⇒ (n²- 9) (n + 10) = 0

$\big[\therefore \text{n} +10 \neq 0\big]$

⇒ n - 9 = 0

⇒ n = 9

Hence, n = 9

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