Dokaži da sljedeća nejednakost vrijedi za sve pozitivne realne brojeve
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
,
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
,
![c](/media/m/e/a/3/ea344283b6fa26e4a02989dd1fb52a51.png)
,
![d](/media/m/f/7/d/f7d3dcc684965febe6006946a72e0cd3.png)
,
![e](/media/m/1/6/f/16f8978af0f3c64c3eb112a539ba73dd.png)
i
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
:
%V0
Dokaži da sljedeća nejednakost vrijedi za sve pozitivne realne brojeve $a$, $b$, $c$, $d$, $e$ i $f$: $$
\sqrt[3]{\frac{abc}{a+b+d}}+\sqrt[3]{\frac{def}{c+e+f}} < \sqrt[3]{(a+b+d)(c+e+f)} \text{.}
$$