Find two consecutive odd positive integers,


Find two consecutive  odd positive integers, sum of whose squares is 290.


We have to find two consecutive integers sum of whose squares is 290.

Let the two consecutive integers be x and x+2

According to the question


$x^{2}+x^{2}+4+4 x=290$

$2 x^{2}+4 x+4=290$

Dividing both sides by 2

$x^{2}+2 x+2=145$

$x^{2}+2 x-143=0$

$x^{2}+13 x-11 x-143=0$





Therefore two consecutive integers are 11,13


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