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Question Number 209316 by klipto last updated on 06/Jul/24

if 2n^2 +3n^3 =n! find n

if2n2+3n3=n!findn

Answered by A5T last updated on 07/Jul/24

n(2+3n)=(n−1)! (n−1)!≤n(2+3n) n(2+3n)≥n(n−1)(n−2) ⇒3n≥n^2 −3n⇒n^2 ≤6n⇒n≤6 Checking⇒n=6

n(2+3n)=(n−1)!(n−1)!⩽n(2+3n)n(2+3n)⩾n(n−1)(n−2)⇒3n⩾n2−3n⇒n2⩽6n⇒n⩽6Checking⇒n=6

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