Question

State true or false:

Two consecutive odd natural numbers such that the sum of their squares is $130$ are $7$ and $10$.

• A. True
• B. False

Answer 1

The correct option is B False

Let the numbers be $(2n-1)$ and $(2n+1)$ then,
$(2n-1{)}^2+(2n+1{)}^2=130$
$4n^2-4n+1+4n^2+1+4n=130$
$8n^2=128$
$n^2=16$
$n=\pm 4$
Neglect the negative value, $n=4$
The numbers are $7,9$