Question 178834
Two positive numbers 
x, y
:
differ by 11,
x-y = 11
or
x = (y+11)
:
 their square roots differ by 1.
{{{sqrt(x) - sqrt(y)}}} = 1
:
 Find the numbers
:
Substitute (y+11) for x in the above equation
{{{sqrt(y+11) - sqrt(y)}}} = 1
:
{{{sqrt(y+11)}}} = {{{sqrt(y)}}} + 1
:
Square both sides
y + 11 = ({{{sqrt(y)}}} + 1)^2
;
FOIL the right side:
y + 11 = y +{{{2sqrt(y)}}} + 1
:
y - y + 11 - 1 = {{{2sqrt(y)}}}
:
10 = {{{2sqrt(y)}}}
:
Square both sides:
100 = 4y
y = {{{100/4}}}
y = 25
then
x = 25 + 11
x = 36
:
This satisfies the problem as you can see