Question

Va rog mult dau coroana cat mai repede

Answer 1

 

$\displaystyle\\\frac{3x}{5}=\frac{2y}{3}=\frac{6z}{7}=k\\\\\texttt{Rezylta ca:}\\\\x=\frac{5k}{3};~~~y=\frac{3k}{2};~~~z=\frac{7k}{6}\\\\x\cdot y\cdot z=630\\\\\frac{5k}{3}\cdot\frac{3k}{2}\cdot\frac{7k}{6}=630\\\\k^3\cdot\frac{5}{3}\cdot\frac{3}{2}\cdot\frac{7}{6}=630\\\\\frac{5\cdot7}{2\cdot6}\cdot k^3=630\\\\\frac{35}{12}\cdot k^3=630\\\\k^3=\frac{630\cdot12}{35}\\\\k^3=18\cdot12\\\\k^3=216\\\\k^3=6^3\\\\\boxed{k=6}$

$\displaystyle\\x=\frac{5k}{3}=\frac{5\cdot6}{3}=5\cdot2=\boxed{\bf10}\\\\y=\frac{3k}{2}=\frac{3\cdot6}{2}=3\cdot3=\boxed{\bf9}\\\\z=\frac{7k}{6}=\frac{7\cdot6}{6}=7\cdot1=\boxed{\bf7}$