SOLUTION: Find two consecutive odd integers such that the sum of their squares is 802.

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Question 1148790: Find two consecutive odd integers such that the sum of their squares is 802.

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
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Let "x" be the EVEN integer number exactly between the two unknown consecutive unknown integer numbers.


Then the unknown odd integer numbers are (x-1) and (x+1),

and the problem says that


    %28x-1%29%5E2 + %28x%2B1%29%5E2 = 802.

Then

    x%5E2+-+2x+%2B+1 + x%5E2+%2B+2x+%2B+1 = 802

    2x%5E2 + 2 = 802

    2x%5E2 = 800

    x%5E2 = 800/2 = 400

    x = +/- sqrt%28400%29 = +/- 20.


Thus, there are two pairs of consecutive integer numbers satisfying the condition.


One pair is (19,21),  The other pair is (-21,-19).    ANSWER

Solved.