SOLUTION: the sum of the squares of two consecutive integers is 365. what are the integers. thx

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: the sum of the squares of two consecutive integers is 365. what are the integers. thx       Log On


   

Question 304253: the sum of the squares of two consecutive integers is 365. what are the integers.
thx
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%29%5E2%2B%28x%2B1%29%5E2=365
x%5E2%2Bx%5E2%2B2x%2B1=365
2x%5E2%2B2x-364=0
2*2*2*7*13=728
7*4=28 13*2=26 so -13 and +28 are the factoring numbers
%282x%2B28%29%28x-13%29=0
x=-14,13
(-14,-13)or(13,14)
checking
%28-14%29%5E2%2B%28-14%2B1%29%5E2=365
196%2B169=365
365=365correct
%2813%29%5E2%2B%2813%2B1%29%5E2=365
196%2B169=365
365=365correct