Question 1209563
<pre>
{{{system(ab=1/2,bc=1/3,ac=1/6)}}}

I don't like manipulating fractions, so I'll do it this way to
minimize such manipulation.
 
Multiply the 1st equation by c, the 2nd by a and the 3rd by b

{{{system(abc=expr(1/2)c,abc=expr(1/3)a,abc=expr(1/6)b)}}}

So

{{{abc=expr(1/2)c=expr(1/3)a=expr(1/6)b}}}

Multiply through by 6

{{{3c=2a=b}}}

Substitute 2a for b in ab=1/2, then get a, b, and c.

{{{matrix(6,1,
ab=1/2,
a(2a)=1/2,
2a^2=1/2,
4a^2=1,
a^2=1/4,
a="" +- 1/2)}}}     {{{matrix(3,1,
ab=1/2,
("" +- 1/2)b=1/2,
b="" +- 1)}}}     {{{matrix(3,1,
3c=b,
3c="" +- 1,
c="" +- 1/3)}}}   

---------------------------------------------------------------

{{{matrix(1,5,

a^2=1/4,",", b^2=1,",", c^2=1/9)}}}

{{{matrix(1,5,

1^""/a^2=4,",", 1^""/b^2=1,",", 1^""/c^2=9)}}}


{{{1^""/a^2 + 1^""/b^2 + 1^""/c^2}}}{{{""=""}}}{{{4+1+9}}}{{{""=""}}}{{{14}}}

Edwin</pre>