Here's the long way. It also gives slightly more information about the number of possible solutions.
So if
then
for some value of n.
We may immediately cancel the n!, giving:
<-- Divide both sides by 6!
<-- Divide both sides by (n - 9)!
Now expand and get everything all to one side:
Our advantage (and only advantage) here in solving this is that we know n must be a positive integer and, to make any sense, .
So let's simply try different values of n one by one until we find a solution. (If you wish to narrow the list a bit, the rational roots theorem says that n must be a factor of 840 as well.) So here we go:
So as ThePerfectHacker said, n = 15 is a solution. By either synthetic or long division, this means that
As it happens that last factor gives only complex values of n, so n = 15 is the only solution.
-Dan
Hello, lkafl!
We have: .i know how to set it up and all
but when I get to a certain point, I got stuck. .I did, too
Clear denominators: .
I'll take baby-steps . . .
Divide by
Divide by 6! . . . . . . [ . Remember that!]
We have:. . . . . .
We have: the product of three consecutive integers is 504.
. . Look familiar? . . . They must be: 7, 8, 9.
Therefore: .