Find Two Numbers by Difference and Difference of Squares Calculator

Welcome to the free online calculator to find two numbers by difference and difference of squares. For example, the difference of two numbers is 8 and the difference of their squares is 160. What are the numbers?

Find Two Numbers by Difference and Difference of Squares Calculator

x - y = a

x² - y² = b

Eg, The difference between two numbers is 8 and the difference of their squares is 160. What are the numbers? Enter 8 in the first input box and enter 160 in the second input box. Then click Calculate button.

Calculate Reset

How to find two numbers based on the difference and difference of squares

Assuming these two numbers are x and y.

Then, we can get two equations based on the above problem description.

x – y = 8………(1)

x² – y² = 160………(2)

Simplify the first equation, and let x be represented by y.

x = 8 + y

Substitute x = 8 + y into the second equation and solve.

x² – y² = 160

(8 + y)² – y² = 160

64 – 16y + y² – y² = 160

64 – 16y = 160

16y = 96

y = 6

Now, put y = 6 into the first equation to get the value of x

x = 8 + y = 8 + 6 = 14

The two numbers are 14 and 6.

Is it right or not? Check it out!

14 – 6 = 8

14² – 6² = 196 – 36 = 160

Yes, this is correct.

There is no difficulty in the whole process, you can try it again. Or just use our free calculator to find two numbers by difference and difference of squares. The calculator omits all steps and displays the answer in milliseconds.

Next, we will introduce how to use the calculator.

How to use the calculator to find two numbers by difference and difference of squares

Using the calculator is simple, follow these 3 steps:

1Enter the difference in the first input box.
2Enter the difference of squares in the second input box.
3Click Calculate button to get the answer, or click Reset button to start a new calculation.

Next, let’s look at some examples.

Solved examples using the calculator to find two numbers by difference and difference of squares

Example 1: The difference between two numbers is 15 and the difference of their squares is 465. What are the numbers?

Enter 15 in the first input box.

Enter 465 in the second input box.

Then click Calculate button, as shown in the figure, the two numbers are 23 and 8.

23 – 8 = 15

23² – 8² = 529 – 64 = 465

The difference between two numbers is 15 and the difference of their squares is 465. What are the numbers?

Example 2: The difference between two numbers is 9 and the difference of their squares is 981. What are the numbers?

Enter 9 in the first input box.

Enter 981 in the second input box.

Then click Calculate button, as shown in the figure, the two numbers are 59 and 50.

59 – 50 = 9

59² – 50² = 3481 – 2500 = 981

The difference between two numbers is 9 and the difference of their squares is 981. What are the numbers?

Find Two Numbers by Difference and Difference of Squares Calculator