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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]

[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

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

many many amounts of solutions one of which is cauchys

you wrote it backwards

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