Question

The sum of square of two consecutive odd number is 514 . Find those numbers

Answer 1

15 and 17 are the numbers

Answer 2

Let the two consecutive odd numbers be x and x+2.

Given that sum of squares of two consecutive odd numbers is 514.

 x^2 + (x+2)^2 = 514

x^2 + x^2 + 4x + 4 = 514

2x^2 + 4x = 510

x^2 + 2x = 255

x^2 + 2x - 255 = 0

x^2 - 15x + 17x - 255 = 0

x(x-15) + 17(x - 15) = 0

(x+17)(x-15) = 0

x = 15,-17.


if x = 15 then x + 2 = 17.

if x = -17 then x + 2 = -15

Hope this helps!