Question

The sum of two consecutive natural numbers and the, squre of the first is 5329. What are the numbers ?

Answer 1

Answer:

72 and 73

Step-by-step explanation:

Let the first natural number be k.

So, consecutive natural number is k +1.

Now, according to the question

$k^{2}  + k + (k+1) =  5329$

or, $k^{2}  + 2k + 1  =  5329$

or, $k^{2}  + 2k - 5328  =  0$  

Now, by splitting the middle term, we get

$k^{2}  + 74k - 72k - 5328  =  0$

or,   $k(k+ 74) -72(k+74) = 0 \\(k-72)(k+74) =   0 \\\\ (k- 72) = 0 , or  (k  + 74) = 0$

⇒  either k = 72 0r k = -74

But, as k is a natural number so k ≠  -74

Hence, k = 72.

So, the consecutive numbers are k and k+1 = 72 and 73