The sum of the squares of two consecutive odd positive integers is 290. Find the numbers. (CBSE 2014)

Let first odd positive integer be x.

⇒ second odd positive integer = x + 2

⇒ x² + (x + 2)² = 290

⇒ x² + x² + 4 + 4x = 290

⇒ 2x² + 4x – 286 = 0

Dividing the whole equation by 2, we get –

⇒ x² + 2x – 143 = 0

⇒ x² + (13 – 11)x – 143 = 0

⇒ x² + 13x – 11x – 143 = 0

⇒ x(x + 13) – 11(x + 13) = 0

⇒ (x – 11)(x + 13) = 0

⇒ x = 11 or x = – 13

But x is a positive integer

⇒ x = 11 is the first odd positive integer.

And, second consecutive odd positive integer = x + 2

= 13