Marinada '26

[lang=hr] Riješi sustav za $x,y,z\in\mathbb{R}^+$: \[ \begin{cases} \dfrac{x^7+y^7}{z^3}+\dfrac{y^7+z^7}{x^3}+\dfrac{z^7+x^7}{y^3}=2x^2y^2+2y^2z^2+2z^2x^2,\\[2mm] (\sqrt{yz}-2)(\sqrt{zx}-4)\le 0. \end{cases} \] Napiši tri intervala za $x$, $y$ i $z$ odvojena zarezima navedenim redoslijedom. Također koristi oble zagrade za opis intervala npr. (6, 10), (6, 67), (67, 667). [/lang] [lang=en] Solve the system for $x,y,z\in\mathbb{R}^+$: \[ \begin{cases} \dfrac{x^7+y^7}{z^3}+\dfrac{y^7+z^7}{x^3}+\dfrac{z^7+x^7}{y^3}=2x^2y^2+2y^2z^2+2z^2x^2,\\[2mm] (\sqrt{yz}-2)(\sqrt{zx}-4)\le 0. \end{cases} \] Write three intervals for $x$, $y$, and $z$, separated by commas in the given order. Also, use parentheses to describe the intervals, e.g., (6, 10), (6, 67), (67, 667). [/lang]