Question 903062
{{{a+b=3}}}
{{{ab=1}}}
Then,
{{{a=1/b}}}
Substituting,
{{{1/b+b=3}}}
{{{1+b^2=3b}}}
{{{b^2-3b+1=0}}}
Complete the square.
{{{b^2-3b+9/4+1=9/4}}}
{{{(b-3/2)^2=9/4-4/4}}}
{{{(b-3/2)^2=5/4}}}
{{{b-3/2=0 +- sqrt(5)/2}}}
{{{b=3/2 +- sqrt(5)/2}}}
So then,
{{{a+(3/2 +- sqrt(5)/2)=3}}}
{{{a=-3/2 +- sqrt(5)/2}}} 
Remember that the +/- symbol changes from {{{a}}} to {{{b}}} 
so if {{{a=-3/2 + sqrt(5)/2}}} then {{{b=3/2 - sqrt(5)/2}}}