Question

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

Answer 1

Answer

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,  

By using the formula of

Then, applying the   formula to

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.

Answer 2

Step-by-step explanation:

15 and 16 is the consecutive no.