Question

The differences of squares of two consecutive natural numbers is 2011 then find the numbers

Answer 1

Let the 1st number be x.
So, 2nd number will be x+1
A. T. Q.
$(x + 1) {}^{2} - {x}^{2} = 2011$
${x}^{2} + 1 + 2x - {x}^{2} = 2011$
$2x + 1 = 2011$
$2x = 2011 - 1$
$2x = 2010$
$x = \frac{2010}{2}$
$x = 1005$
$Therefore, 1st \:number = 1005$
$2nd \:number = 1005+1 = 1006$

⭐⭐✔$\bf{THANKS}$✔⭐⭐

Answer 2

Let First consecutive natural number be X.



Second consecutive natural number = ( X + 1 ).



According to the question,


( X + 1 )² - X² = 2011



X² + 1 + 2X - X² = 2011



2X + 1 = 2011


2X = 2011 - 1


2X = 2010


X = 1005



First number = X = 1005


And,


Second number = X + 1 = 1006.