Question

State the following statement is True or False

If the sum of the squares of two consecutive even natural numbers is $100$, then the numbers are $8$ and $6$.

• A. True
• B. False

Answer 1

The correct option is A True

Let the numbers be $2n$ and $2n+2$
Thus,
$(2n{)}^2+(2n+2{)}^2=100$
$4n^2+4n^2+4+8n=100$
$8n^2+8n-96=0$
$n^2+n-12=0$
$n^2+4n-3n-12=0$
$(n+4)(n-3)=0$
$n=-4,3$
Neglecting the negative number, $n=3$
Thus numbers are $6$ and $8$