Fm -proof

[static quiver]

try expand and simplify the expression

[tame phoenix]

the way to get some sort of inequality is to realise that squares are nonnegative so that expression >= 0

[rare moat]

ah that's actually a really nice problem

[tame phoenix]

It really is

But would you ever get smth like it

Where’s it from?

[heady crescent]

dk, teacher gave the question for us to do

and i dk where to start

[static quiver]

@heady crescent

[heady crescent]

i did and it doesnt look like im getting any where

[rare moat]

ignore doing anything for now and lets first establish that the expression must be >= 0 since it's a bunch of squares added together

i'm gonna call alpha a, beta b and gamma g for convenience but if we expand now we're going to get
2(a^2 + b^2 + g^2) - 2(sum of ab) >= 0
sum of ab = n (roots of polynomials)
so 2(a^2 + b^2 + g^2) >= 2n
we can't really deal with a^2 + b^2 + g^2 like this so why don't we rewrite it as (a+b+g)^2 - 2(sum of ab)

[heady crescent]

Thanks, I got it now.