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Find the value of 'n' if (n+4) ! = 56...

Find the value of 'n' if
`(n+4) ! = 56 (n+2) !`.

A

`3`

B

`5`

C

`4`

D

`6`

Text Solution

Verified by Experts

The correct Answer is:
`C`
`(n +4)! = 56.(n+2)!`
`rArr (n+4) (n+3) (n+2) ! = 56. (n+2) !`
`rArr (n+4) (n+3) = 56`
`rArr n^(2) +7n +12 - 56 = 0`
`rArr n^(2) +7n - 44 = 0`
`rArr (n+11) (n-4) = `
`rArr n +11 = 0` or `n - 4 = 0`
`rArr n = - 11` or `n = 4`
But n cannot be negative.
`:. n = 4`.
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