Question

The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers. 

Answer 1

Let the two consecutive positive odd numbers be x and (x+2).
According to the given condition 

`x^2+(x+2)^2=514` 

⇒`x^2+x^2+4x+4=514` 

⇒`2x^2+4x-510=0` 

⇒`x^2+2x-255=0` 

⇒`x^2+17x-15x-255=0` 

⇒`x(x+17)-15(x+17)=0` 

⇒`(x+17)(x-15)=0` 

⇒`x+17=0`  or  `x-15=0` 

⇒`x=-17  or  x-15` 

∴`x=15`                    (x is a positive odd number) 

When `x=15` 

`x+2=15+2=17` 

Hence, the required positive integers are 15 and 17.