Question 911831
Two numbers, x and y;
x+y=10 and  xy=5;
First goal is solve for x and y.  


{{{x(10-x)=5}}}
{{{-x^2+10x-5=0}}}
{{{x^2-10x+5=0}}} not factorable.


{{{x=(10+-sqrt(100-4*5))/2}}}
{{{x=(10+-sqrt(80))/2}}}
{{{x=(10+-(sqrt(2*2*2*2*5))/2}}}
{{{x=(10+-4sqrt(5))/2}}}
{{{highlight(x=5+-2sqrt(5))}}}


{{{highlight_green(y=10-x)}}}
{{{y=10-5+-2sqrt(5)}}}
{{{highlight(y=5+-2sqrt(5))}}}


<s>x and y are equal</s>.  You will want to rationalize the denominators when looking for their reciprocal.  Actually, one number  (either x or y) would take the positive square root and the other number will take the negative square root.