Question

if (n+2)!=462(n)! option a=10 b 15 c 20
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Answer 1

Given:

(n+2)! = 462 (n)!

=> (n+2)(n+1)(n)! = 462 (n)!

=> (n+2)(n+1) = 462 (as (n)! on both sides cancel each other)

=> n(n+1) +2(n+1) = 462

=> n²+n+2n+2 = 462

=> n²+3n+2= 462

=> n²+3n-460= 0

=> n²+23n-20n-460= 0

=> n(n+23)-20(n+23)= 0

=> (n-20)(n+23)= 0

Therefore,

n = -23 and n = 20

As n cannot be negative, so n= 20 is the answer.

c) 20 is the right one.