i know how to set it up and all but when I get to a certain point... I got stuck..
Help please?
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: .