SOLUTION: Find two consecutive odd integers such that the sum of their squares is 650.

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Question 1179475: Find two consecutive odd integers such that the sum of their squares is 650.

Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the EVEN number half way between the two unknown consecutive odd numbers.


Then your equation is


    %28x-1%29%5E2 + %28x%2B1%29%5E2 = 650

    x^2 - 2x + 1 + x^2 + 2x + 1 = 650

    2x^2 + 2 = 650

    2x^2 = 650-2 = 648

     x^2         = 648/2 = 324

     x = sqrt%28324%29 = +/- 18.


So, for x we have two values 18 and - 18.


They give two pairs of solutions to the problem: (17,19)  and  (-19,-17).    ANSWER

Solved.