Well at first glance, I'd say you could just work out p^2, simplify as far as possible and then q and r come very easily by swapping a for b, b for c etc. rather than squaring each one separately then adding together.
(Original post by Blazy)
I've put this under Sixth Form but it's just an interesting question I found.
Any neat way of doing this? I Seeing as it looks quite cyclical (not sure if this is the word), I assume there must be a neat way of doing this.
I considered some mindless algebra bashing via
but it looks messy, though
does come out quite nicely. I've looked at it in some kind of matrix form but nothing sticks out.
That's the best thing I can see so far - not sure about anything easier. But in fact; you could just work out p^2.
which gives you:
Then where you get ab, write ab + ac + bc (because you'll get ac + bc from q and r)
Then do the same with ab and bc, then you can write a^2 + b^2 + c^2 where we have a^, b^2 OR c^2 above.
Then that's basically done. You'll find it simplifies very nicely (well it looks like it will to me).
EDIT: I did the simplifying from where I got and it comes out VERY nicely:
Last edited by Intriguing Alias; 26-06-2012 at 11:25.
Reason: Missed a LOT of squares
Yep sorry - that should've been a^2 where I wrote a and so on
(Original post by nuodai)
Something doesn't seem right here. The only terms contributing to the
, and so the coefficient of
I reckon there's an easier way around this than expansion and simplification. For instance, we know that
is an even quartic (it's obviously quartic, and we can check that it's even by considering signs of terms without needing to calculate it explicitly). A bit more rummaging in this direction might lead you to an answer.
Despite the error though, that took me a fairly small amount of time, I started just after making the initial post and finished at about 20 to 11.
Last edited by Intriguing Alias; 26-06-2012 at 11:27.