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Question

If (n+2)!=60[(n1)!], find n.

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Solution

(n+2)!=60(n1)!(n+2)(n+1)n(n1)!=60(n1)!n(n+1)(n+2)=60n(n2+3n+2)=60n3+3n2+2n60=0(n3)(n2+6n+20)=0

n=3, since n2+6n+20 has imaginary zeroes
Therefore, n=3

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