Question

find the two consecutive odd natural numbers,the sum of those squares is 202

Answer 1

9 and 11 are the two consecutive odd numbers whose sum of their squares is 81+121=202

Answer 2

Let the two consecutive numbers be x and x+2.   --- (1)

Given that Sum of squares = 202

                  (x)^2 + (x+2)^2 = 202

                   x^2 + x^2 + 4x + 2x = 202

                   2x^2 + 4x + 2x = 202

                   2x^2 + 4x - 198 = 0

                   2(x^2 + 2x - 99) = 0

                    x^2 + 2x - 99 = 0

                     (x+11)(x-9) = 0

                      x = 9 (or) x = -11.

Substitute the values in (1), we get x = (9,11).