Question

Aflati numerele x,y,z stiind ca sunt invers proportionale cu nr 1,(3);6.(6);0(4) iar x+y+z=1134 rezolvare completa

Answer 1

[tex]\{x,y,z\} ip\{1,(3);6,(6);0,(4)\}\Rightarrow \frac{\frac{x}{1}}{\frac{4}{3}}=\frac{\frac{y}{1}}{\frac{20}{3}}=\frac{\frac{z}{1}}{\frac{4}{9}}\Rightarrow \\ \\ \Rightarrow \frac{x}{\frac{3}{4}}=\frac{y}{\frac{3}{20}}=\frac{z}{\frac{9}{4}}=k\Rightarrow x=\frac{3k}{4} ,y=\frac{3k}{20},z=\frac{9k}{4}\\ x+y+z=1134\\ \frac{3k}{4}+\frac{3k}{20}+\frac{9k}{4}=1134|\cdot 20\\ 15k+3k+45k=22680\\ 63k=22680\\ \boxed{\boxed{k=360}}\\ x=\frac{3k}{4}=\boxed{270}\\ y=\frac{3k}{20}=\boxed{54}\\ [/tex]
$z=\frac{9k}{4}=\boxed{810}$