If $x$, $y$ and $z$ satisfy $xy=1$, $yz=2$ and $xz=3$, what is the value of $x^2+y^2+z^2$? Express your answer as a common fraction. 
If $x$, $y$ and $z$ satisfy $xy=1$, $yz=2$ and $xz=3$, what is the value of $x^2+y^2+z^2$?  Express your answer as a common fraction.


I tried going along the path of computing $(x+y+z)^2$, which expands to $(x^2+y^2+z^2) + 2\cdot (xy+yz+xz)$, but I couldn't go anywhere from there (other than substituting xy, yz, xz, but that's not enough information.

$$\text{Compilation of all *Hints*}$$
We know that $$(x+y+z)=xyz(\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx})$$
From here we see that $$(x+y+z)=xyz(\frac{11}{6})$$
Also, $(xyz)^2=6$ , so it would be nice to say that
$$(x+y+z)^2=6\big(\frac{11}{6}\big)^2$$
Then write the expansion for $$(x+y+z)^2$$ and keep substituting till you get the answer.
