[tex] \frac{x}{2}=\frac{y}{3}= \frac{z}{7}; xy=54 ;x= \frac{54}{y} \\ \\ \frac{x}{2}=\frac{y}{3};x= \frac{2}{3}y \\ \\ \frac{54}{y}= \frac{2y}{3} \\ \\ 2y^{2} =3\cdot54 \\ \\ y ^{2} =81 \\ \\ y= \sqrt{81} ; y=9 \\ \\ \frac{x}{2}=\frac{z}{7};x= \frac{2}{7}z ; x= \frac{54}{y} \\ \\ \frac{2z}{7}= \frac{54}{y} \\ \\ \frac{2z}{7}= \frac{54}{9} \\ \\ z= \frac{7\cdot54}{2\cdot9}=21 \\ \\ x=\frac{54}{y} = \frac{54}{9}=6 \\ \\ x=6;y=9, z=21 [/tex]
