<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. You can take the equations pairwise. For example, you have $xy=1$ and $yz=2$. So for example,
$$
\dfrac{1}{2}= \dfrac{xy}{yz}=\dfrac{x}{z}
$$
But then $z=2x$. But you know $xz=3$. Can you substitute and find $x$ or $z$? Can you repeat this process for $y$? Knowing their values it should be routine to find $x^2+y^2+z^2$.
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