<PRE><B>Question 500575</B>
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 &amp; 16 are the integers
:
:
See if that works
15^2 + 16^2 =
225 + 256 = 481</PRE>