Question

The difference between the squares of two consecutive numbers is 31. Find the numbers

Answer 1

Let 1st con number x
Let 2nd con. number x+1
So,
x+x+1=31
2x+1=31
2x=31-1
x=30/2
x=15
1st con number=x=15
2nd con number=x+1=15+1=16

Answer 2

15 and 16 are the two consecutive numbers.

Given:

The difference of the square of two consecutive numbers is 31.

To find:

The two consecutive numbers.

Solution:

From the question, we can understand that the difference between the two numbers is 1.

And the difference between their square is 31.

We can take that the two numbers are x and x+1.

From the question,  

$(x+1)^{2}-x^{2}=31$

By using the formula of $(a+b)^{2}=a^{2}+b^{2}+2 a b$

Then, applying the $(a+b)^{2}$  formula to $(x+1)^{2}$

We can get,

$\begin{array}{c}{x^{2}+1^{2}+(2 \times x \times 1)-x^{2}=31} \\ {x^{2}+1^{2}+2 x-x^{2}=31}\end{array}$

$\begin{array}{c}{2 x+1=31} \\ {2 x=31-1} \\ {2 x=30} \\ {x=15}\end{array}$

And the second number is x+1=15+1

x+1=16

And the numbers are 15 and 16.