Question

The sum of the squares of two consecutive positive integers is 365. Find the integers. 

 

Answer 1

Let the required two consecutive positive integers be x and (x+1).
According to the given condition,  

`x^2+(x+1)^2=365` 

⇒`x^2+x^2+2x+1=365` 

⇒`2x^2+2x-364=0` 

⇒`x^2+x-182=0` 

⇒`x^2+14x-13x-182=0` 

⇒`x(x+14)-13(x+14)=0` 

⇒`(x+14)(x-13)=0` 

⇒`x+14=0  or  x-13` 

∴`x=13`            (x is a positive integers) 

When `x=13` 

`x+1=13+1=14` 

Hence, the required positive integers are 13 and 14.