Question

The sum of the square of 2 consecutive odd positive integers is 290.Find them.

Answer 1

Let the numbers be X and X+ 2. Then as per question, 

X² + (X+ 2)²= 290 

⇒ 2x² + 4X - 286 = 0

⇒ X² + 2X - 143 = 0 

⇒ X² + 13X - 11X -143 = 0 

⇒ X (X +13)-11(X +13) = 0  

⇒ (X+13 )(X-11) = 0.  X can't be negative number as its natural number. 

Hence, X = 11and X+ 2= 13.