Question 1004438
{{{system(x+y=15,xy=5)}}} and you are interested in finding {{{1/x+1/y}}}.


To begin,  {{{x(15-x)=5}}}
{{{15x-x^2=5}}}
{{{x^2-15x+5=0}}}


{{{x=(15+- sqrt(15^2-4*5))/2}}}


{{{x=(15+- sqrt(225-20))/2}}}


{{{x=(15+- sqrt(205))/2}}}


The two numbers are  {{{(15-sqrt(205))/2}}} and {{{(15+sqrt(205))/2}}}.
A little more arithmetic to find the answer to the question.