SOLUTION: solve the following question: n!/(n-2)!=72

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Question 980743: solve the following question:
n!/(n-2)!=72
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
n%21%2F%28n-2%29%21=72
since
n%21=n%28n-1%29%28n-2%29%28n-3%29…… and
%28n-2%29%21=%28n-2%29%28n-3%29……
we have
%28n%28n-1%29%28n-2%29%28n-3%29%29%2F%28%28n-2%29%28n-3%29%29=72

n%28n-1%29=72
n%5E2-n=72
n%5E2-n-72=0
n%5E2%2B8n-9n-72=0
%28n%5E2%2B8n%29-%289n%2B72%29=0
n%28n%2B8%29-9%28n%2B8%29=0
%28n-9%29%28n%2B8%29=0
solutions:
%28n-9%29=0=>n=9
%28n%2B8%29=0=>n=-8...disregard negative solution, n%21 is a sequence with integer values for non-negative n
so, your answer is n=9