SOLUTION: Find the positive integer n such that P(n+1,3)=10 P(n-1,2)

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Question 1138723: Find the positive integer n such that P(n+1,3)=10 P(n-1,2)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


P(n+1,3) = (n+1)(n)(n-1)
P(n-1,2) = (n-1)(n-2)

So

%28n%2B1%29%28n%29%28n-1%29+=+10%28n-1%29%28n-2%29
%28n%2B1%29%28n%29+=+10%28n-2%29
n%5E2%2Bn+=+10n-20
n%5E2-9n%2B20+=+0
%28n-5%29%28n-4%29+=+0

There are two solutions: n=5 and n=4.

n=5:
P(6,3) = 6*5*4 = 120
P(4,2) = 4*3 = 12
10*12 = 120

n=4:
P(5,3) = 5*4*3 = 60
P(3,2) = 3*2 = 6
10*6 = 60