Marinada '25

[lang=hr] Ivica, koji već razmišlja o prstenu koji će kupiti Marici jer je siguran da će ju apsolutno očarat, nastavlja sa smišljanjem zadataka: Ako je \[ x+y+z=10 \] \[ x^2+y^2+z^2=11^2 \] \[ x^{-1}+y^{-1}+z^{-1}=12^{-1} \] Koliko iznosi $x^3+y^3+z^3$? [/lang] [lang=en] Ivica, who is already thinking about the ring he will buy for Marija because he is sure it will absolutely charm her, continues inventing problems: Given \[ x+y+z=10 \] \[ x^2+y^2+z^2=11^2 \] \[ x^{-1}+y^{-1}+z^{-1}=12^{-1} \] Find the value of \( x^{3} + y^{3} + z^{3}. \) [/lang]