Question

If $x+y+z=6,xy+xz+yz=11,xyz=6$,
then $\frac{x}{yz}+\frac{y}{xz}+\frac{z}{xy}$ equals

• A. $\frac{7}{3}$
• B. $\frac{13}{6}$
• C. $\frac{5}{3}$
• D. $\frac{6}{11}$

Answer 1

The correct option is A

$\frac{7}{3}$

$\frac{x}{yz}+\frac{y}{zx}+\frac{z}{xy}=\frac{x^2+y^2+z^2}{xyz}$
$=\frac{(x+y+z)-2(xy+yz+zx)}{xyz}$
$=\frac{6^2-2\times 11}{6}=\frac{14}{6}=\frac{7}{3}$