Question 799680
The two numbers are x and y.
{{{(x+y)/2=5}}} and {{{sqrt(xy)=3}}}.


{{{x+y=2*5=10}}}
{{{y=10-x}}}
Substitute.
{{{sqrt(x(y))=sqrt(x(10-x))=3}}}
{{{sqrt(10x-x^2)=3}}}
Square both sides.
{{{10x-x^2=9}}}
{{{10x-x^2-9=0}}}
{{{x^2-10x+9=0}}}
{{{(x-9)(x-1)=0}}}


x=9 or x=1
y=10-9 or y=10-1
y=1 or y=9


ANSWER:  Either way, the two numbers are 9 and 1.