Question

What is sum of two consecutive numbers difference of whose square is 19?

Answer 1

Answer:

Let the two consecutive no be x and x+1 respectively

According to question

The difference of their square is 19

i. E (x+1)^2 - x^2=19

x^2 +1 +2x - x^2=19

1 +2x =19

2x=19-1

2x=18

x=18/2

x=9

1st no is 9

2nd ni is 9+1 =10

The sum of two numbers is 9+10 =19

Answer 2

Solution:

Given:

=> Difference of square of two consecutive numbers = 19

To Find:

=> Sum of two consecutive numbers.

So,

Let two consecutive numbers be (x) and (x - 1).

Now, According to question

$\sf{\implies (x+1)^{2}-x^{2}=19}$

$\sf{\implies x^{2}+1+2x-x^{2}=19}$

$\sf{\implies 2x+1=19}$

$\sf{\implies 2x=18}$

$\sf{\implies x = \dfrac{18}{2}}$

$\sf{\implies x=9}$

So, Two consecutive numbers are,

=> x = 9

=> x + 1 = 10

Now. the sum of two consecutive numbers are,

=> (x + 1) + x

=> 10 + 9

=> 19

Hence, the sum of two consecutive numbers be 19.