Question 1071818
Let {{{x}}} and {{{y}}} be the two numbers.
We are told that
{{{x+y=20}}} and {{{x*y=20}}} ,
and we are asked to find
{{{a=1/x+1/y}}} .
From {{{x*y=10}}} we get
{{{x=10/y}}} and {{{y=10/x}}} .
Substituting those expressions
for {{{x}}} and {{{y}}}
in {{{x+y=20}}} , we get
{{{10/y+10/x=20}}}
{{{10(1/y+1/x)=20}}}
Does the expression in brackets look familiar?
It is {{{a=1/x+1/y}}} .
So, {{{10a=20}}} ,
{{{a=20/10}}} , and
{{{highlight(a=2)}}} .
You could solve for {{{x}}} and {{{y}}} ,
but it will be ugly.