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) (Show Source): You can put this solution on YOUR website!
Two positive numbers
x, y
:
differ by 11,
x-y = 11
or
x = (y+11)
:
their square roots differ by 1.
= 1
:
Find the numbers
:
Substitute (y+11) for x in the above equation
= 1
:
= + 1
:
Square both sides
y + 11 = ( + 1)^2
;
FOIL the right side:
y + 11 = y + + 1
:
y - y + 11 - 1 =
:
10 =
:
Square both sides:
100 = 4y
y =
y = 25
then
x = 25 + 11
x = 36
:
This satisfies the problem as you can see
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