Question

aflati numerele x, y, z apartin lui N stiind ca x/8=y/6=10/z

Answer 1

 

$\displaystyle\bf\\\frac{x}{8}=\frac{y}{6}=\frac{10}{z}\\\\\text{Avem 3 cazuri:}\\Cazul~1:~~~Fractiile~sunt~echiunitare~(o~varianta).\\\\\frac{x}{8}=\frac{y}{6}=\frac{10}{z}=1\\\\x=8\\y=6\\z=10\\\\Cazul~2:~~~Fractiile~sunt~supraunitare~(3~variante).\\\\Folosim~divizorii~1,~2~si~5~ai~lui~10.\\Varianta~1:\\\\\frac{x}{8}=\frac{y}{6}=\frac{10}{z}=10\\\\x=10\cdot8=80\\y=10\cdot6=60\\z=\frac{10}{10}=1$

$\displaystyle\bf\\Varianta~2:\\\\\frac{x}{8}=\frac{y}{6}=\frac{10}{z}=5\\\\x=5\cdot8=40\\y=5\cdot6=30\\z=\frac{10}{5}=2\\\\Varianta~3:\\\\\frac{x}{8}=\frac{y}{6}=\frac{10}{z}=2\\\\x=2\cdot8=16\\y=2\cdot6=12\\z=\frac{10}{2}=5\\\\\\Cazul~3:~~~Fractiile~sunt~subunitare~(o~varianta).\\Folosim~divizorul~comun~2~al~lui~8~si~6.\\\\\frac{x}{8}=\frac{y}{6}=\frac{10}{z}=\frac{1}{2}\\\\x=\frac{8}{2}=4\\\\y=\frac{6}{2}=3\\\\z=10\cdot2=20$