Question

The sum of two consecutive natural number and the square of the first is $5329$. what are the numbers?

Answer 1

Let the two consecutive natural numbers be $a$ and $a+1$.

According to the question,

$\Rightarrow$ $a+(a+1)+a^2=5329$

$\Rightarrow$ $2a+1+a^2=5329$

$\Rightarrow$ $a^2+2a+1=5329$

$\Rightarrow$ $(a+1{)}^2=5329$

$\Rightarrow$ $a+1=73$

$\Rightarrow$ $a=72$

Thus, the two numbers are $72$ and $73$.