Roots- tricky Inequality question

I have no idea what question you are asking - can you express it symbolically?

I asked Tenofthem.
However somebody could still help a lot.

Ok... Let a,b,c be real numbers such that a^2+b^2+c^2=12. Find the maximum value of
Currant Proofathon question (Q 5)
This is going against the honour code btw.
I used autograph and found the answer was however do not know how to prove the answer is the maximum value it can be mathematically.

what level is this?

i was thinking lagrange multipliers to maximise your function subject to the constraint a^2+b^2+c^2=12, but there's probably a more elegant method involving some work with the symmetry of the function

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There is a very elegant method called autograph and other 3D graph plotters which show the answer in a picture. However, if you want to go against logic (and intrinsically what mathematicians like to do ( work things easily) then it's a higher level- I would guess.
Your way looks better. - However could my idea still prove no higher number than 288 intersects the other graph (the constraint) .

Ok... Let a,b,c be real numbers such that a^2+b^2+c^2=12. Find the maximum value of

This certainly looks BMO-ish, so way out of my league, but I note that both expressions are symmetric under permutation of the variables, so I'm wondering if you can come up with a nice argument that we must have a=b=c for an extremum.

...

Hey, I told you about that (although I never actually do it)
Is it from proofathon?

Found it! : http://www.proofathon.org/Pages/ongoing_contest.php Hm, an on-going contest. Not to worry though; they're from AoPS, they'll never find us here! (And you can submit my solution if you want, just saying.)