Question

The sum of the squares of two consecutive natural numbers is 113. then the numbers are

• A. $8and9$
• B. $7and8$
• C. $6and7$
• D. $5and6$

Answer 1

The correct option is B $7and8$

Let the numbers be $n$ and $n+1$
then $n^2+(n+1{)}^2=113$
$2n^2+2n-112=0$
$n^2+n-56=0$
$n^2+8n-7n-56=0$
$(n+8)(n-7)=0$
$n=7,-8$
Neglect the negative value.
Numbers are $7$ and $8$.