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I'll post the solution now.
This literally took forever to type out in Latex! I have put a spoiler on just in case anyone is still working on the problem. If so, your first hint is to write the roots as k, n-k and n.

There may be a much more elegant way to do this, but my method is certainly correct.

Spoiler

Original post by Khallil
That's a pretty nice method! What did you think of my one?



I personally would say that our methods are similar. As a matter of fact, they are identical once you eliminate your a_2 * a_3 (I just tried your method).

In terms of length, I'd say they are relatively similar, yours may be slightly shorter. Still, on paper, mine was only half a page.

Your method is nice. Although, at first I was puzzled as to where your 1=1 came from, but then I realised haha!
i have no idea how people do that latex stuff and write solutions in that neat way.


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Original post by physicsmaths
i have no idea how people do that latex stuff and write solutions in that neat way.


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Did you do the solution in the end?
Original post by DomStaff
Did you do the solution in the end?


yh i did it a didfferent way. i used factorisation etc


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Original post by physicsmaths
yh i did it a didfferent way. i used factorisation etc


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Post your solution so we don't have to guess your solution! I always like to see an alternative method.

You'll be fine with Latex, if you really can't be bothered with it, just write it normally, like (a/b) or b^(3) or whatever.
Original post by DomStaff
Post your solution so we don't have to guess your solution! I always like to see an alternative method.

You'll be fine with Latex, if you really can't be bothered with it, just write it normally, like (a/b) or b^(3) or whatever.

basically looking at my solution you guys have used standard results where i have had to derive those results. So i have had a hefty amount of working before hand. Then used them results tonprove the rest.


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basically
Let the equation be rewritten as an equation with roots alpha, beta , alpha+beta.
hence it can be written as
a(x-alpha)(x-beta)(x-(alpha+beta))
upon expansion prove what alpha and beta must equal i e (-b/a) then its simple from there on. My solution is more along the lones of the other guy. The first solution that was put up.


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Original post by physicsmaths
basically
Let the equation be rewritten as an equation with roots alpha, beta , alpha+beta.
hence it can be written as
a(x-alpha)(x-beta)(x-(alpha+beta))
upon expansion prove what alpha and beta must equal i e (-b/a) then its simple from there on. My solution is more along the lones of the other guy. The first solution that was put up.


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khalil is his name.


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