SOLUTION: The sum of the squares of two consecutive positive integers is 481. Find the integers.

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Question 500575: The sum of the squares of two consecutive positive integers is 481. Find the integers.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The sum of the squares of two consecutive positive integers is 481. Find the integers.
:
x^2 + (x+1)^2 = 481
FOIL
x^2 + x^2 + 2x + 1 = 481
:
2x^2 + 2x + 1 - 481 = 0
2x^2 + 2x - 480 = 0
simplify, divide by 2
x^2 + x - 240 = 0
Factors to
(x+16)(x-15) = 0
positive solution
x = 15 & 16 are the integers
:
:
See if that works
15^2 + 16^2 =
225 + 256 = 481