SOLUTION: Two positive numbers differ by 11, and their square roots differ by 1. Find the numbers

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Question 178834: Two positive numbers differ by 11, and their square roots differ by 1. Find the numbers
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two positive numbers
x, y
:
differ by 11,
x-y = 11
or
x = (y+11)
:
their square roots differ by 1.
sqrt%28x%29+-+sqrt%28y%29 = 1
:
Find the numbers
:
Substitute (y+11) for x in the above equation
sqrt%28y%2B11%29+-+sqrt%28y%29 = 1
:
sqrt%28y%2B11%29 = sqrt%28y%29 + 1
:
Square both sides
y + 11 = (sqrt%28y%29 + 1)^2
;
FOIL the right side:
y + 11 = y +2sqrt%28y%29 + 1
:
y - y + 11 - 1 = 2sqrt%28y%29
:
10 = 2sqrt%28y%29
:
Square both sides:
100 = 4y
y = 100%2F4
y = 25
then
x = 25 + 11
x = 36
:
This satisfies the problem as you can see