for a,b,c real positive numbers, show that
((a+b)(b+c)(c+a))/ ((a+b+c)^3) <= 8/27
i'm thinking of cuberoot both sides..what do u guys think?
or is there any theorem?
hmm i'm not sure it's true... this is the route i went down:
let d = max(a,b,c) and e = min(a,b,c)
then
{your LHS} <= (d+d)(d+d)(d+d)/(e+e+e)^3 = ((2d)^3)/((3e)^3)
=8d^3/27e^3 = (8/27) * (d/e)^3
But e <= d so the upper bound can be more than 8/27...
You sure its true?
Si