Easy inequality

[zefuri]

Let [unparseable or potentially dangerous latex formula] be positive real numbers such that

[unparseable or potentially dangerous latex formula]

Prove that

[unparseable or potentially dangerous latex formula]

[bradp]

[unparseable or potentially dangerous latex formula] would be the maximum of the RHS... i think. and that makes it equal to the LHS. any other a,b,c,d would make the RHS smaller.
for example [unparseable or potentially dangerous latex formula]
but the squares in the first statement might screw that up
i'll leave proving it up to those with extensive knowledge of Simon's Favorite Factoring Trick

[stupidityismygam]

you found the equality case :) that is a good start

since the equality case is a=b=c=d, i bet there is an AM-GM solution

[zefuri]

many many amounts of solutions one of which is cauchys

[stupidityismygam]

[zefuri]

you wrote it backwards

[stupidityismygam]

it doesnt take away from the strategy...so live with it


if you want to write it correctly... you can c/p and write it properly :) :)

i am lazy