SOLUTION: Two positive numbers differ by 6, and their squares differ by 96. Find the numbers.
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Question 322955: Two positive numbers differ by 6, and their squares differ by 96. Find the numbers.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two positive numbers differ by 6,
x - y = 6
x = (y+6)
:
and their squares differ by 96.
x^2 - y^2 = 96
:
replace x with (y+6)
(y+6)^2 - y^2 = 96
:
FOIL (y+6)(y+6)
y^2 + 12y + 36 - y^2 = 96
:
Combine like terms
y^2 - y^2 + 12y = 96 - 36
:
12y = 60
y =
y = 5
then
x = 5 + 6
x = 11
:
:
Check solution by finding the squares
11^2 - 5^2 = 96
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