Find n, if (n + 3)! = 110 × (n + 1)! - Mathematics and Statistics

Advertisements
Advertisements
Sum

Find n, if (n + 3)! = 110 × (n + 1)!

Advertisements

Solution

(n + 3)! = 110 × (n + 1)!

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

∴ (n + 3)(n + 2) = 110

∴ n2 + 5n + 6 = 110

∴ n2 + 5n + 6 − 110 = 0

∴ n2 + 5n − 104 = 0

∴ n2 + 13n − 8n − 104 = 0

∴ n(n + 13) − 8(n + 13) = 0

∴ (n + 13)(n − 8) = 0

∴ n + 13 = 0 or n − 8 = 0

∴ n = − 13 or n = 8

But n ∈ N

∴ n ≠ − 13

Hence, n = 8.

Concept: Concept of Factorial Function
  Is there an error in this question or solution?
Chapter 6: Permutations and Combinations - Exercise 6.2 [Page 74]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.2 | Q 7. (ii) | Page 74
Share
Notifications



      Forgot password?
Use app×