Question

The sum of the squares of five consecutive natural numbers is $1455$, then numbers are $15,16,17,18,19$.

State whether the given statement is true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Let the five consecutive integers be $n,n+1,n+2,n+3,n+4$
then, $n^2+(n+1{)}^2+(n+2{)}^2+(n+3{)}^2+(n+4{)}^2=1455$
$5n^2+20n+30-1455=0$
$5n^2+20n-1425=0$
$n^2+4n-285=0$
$n=\frac{-4\pm \sqrt{16+1140}}{2}$ $=\frac{-4\pm 34}{2}=15,-17$
Hence, the numbers are $15,16,17,18,19$