Question

The sum of the squares of two consecutive positive even numbers is 452. Find the numbers. 

 

Answer 1

Let the two consecutive positive even numbers be x and x  2.
According to the given condition, 

`x^2+(x+2)^2=452` 

⇒`x^2+x^2+4x+4=452` 

⇒`2x^2+4x-448=0` 

⇒`x^2+2x-224=0` 

⇒`x^2+16x-14x-224=0` 

⇒`x(x-16)-14(x-16)=0` 

⇒`(x+16)(x-14)=0` 

⇒`x+16=0  or  x-14=0` 

⇒`x=-16  or  x=14` 

∴ `x=14`  (x is a positive even number) 

When `x=14` 

`x+2=14+2=16` 

Hence, the required numbers are 14 and 16.