<s>[INST] 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.
 [/INST] Hint: $$(xy)(yz)(xz)=(xyz)^2,$$
take square root, then divide by $xy$ or $yz$ or $xz$ to find $z,\,x,\,y$ respectively.
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