Odredi najveći
![d \in \mathbb{R}](/media/m/0/e/7/0e7f0b4e9901ebc5b72db4aefe43961f.png)
takav da za sve
![a,b,c>0](/media/m/c/1/2/c120cac4a95a480784a6bde53d76635c.png)
takve da je
![a+b+c=1](/media/m/e/c/b/ecbe193e63c2420fe42a6fcfe8a77bf8.png)
minimalna vrijednost izraza
![a^3+b^3+c^3+abcd](/media/m/4/f/3/4f3fd39e2bfa241586b58b9fec20e9b1.png)
iznosi
![\dfrac{1}{4}](/media/m/4/c/d/4cd9dc975677a52018f3927214e6bb9f.png)
.
Determine the greatest
![d \in \mathbb{R}](/media/m/0/e/7/0e7f0b4e9901ebc5b72db4aefe43961f.png)
such that for all
![a,b,c>0](/media/m/c/1/2/c120cac4a95a480784a6bde53d76635c.png)
that satisfy
![a+b+c=1](/media/m/e/c/b/ecbe193e63c2420fe42a6fcfe8a77bf8.png)
the minimal value of the expression
![a^3+b^3+c^3+abcd](/media/m/4/f/3/4f3fd39e2bfa241586b58b9fec20e9b1.png)
equals
![\dfrac{1}{4}](/media/m/4/c/d/4cd9dc975677a52018f3927214e6bb9f.png)
.
[lang=hr]
Odredi najveći \(d \in \mathbb{R}\) takav da za sve \(a,b,c>0\) takve da je \(a+b+c=1\) minimalna vrijednost izraza \(a^3+b^3+c^3+abcd\) iznosi \(\dfrac{1}{4}\).\\
[/lang]
[lang=en]
Determine the greatest \(d \in \mathbb{R}\) such that for all \(a,b,c>0\) that satisfy \(a+b+c=1\) the minimal value of the expression \(a^3+b^3+c^3+abcd\) equals \(\dfrac{1}{4}\).
[/lang]