Find Two Numbers by Sum and Difference of Squares Calculator

Welcome to the free online calculator to find two numbers by sum and difference of squares. For example, the sum of two numbers is 25 and the difference of their squares is 125. What are the numbers?

Assuming these two numbers are x and y.

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

x + y = 25………(1)

x² – y² = 125………(2)

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

x = 25 – y

Substitute x = 25 - y into the second equation and solve.

x² – y² = 125

(25 – y)² – y² = 125

625 – 50y + y² – y² = 125

625 – 50y = 125

50y = 500

y = 10

Now, put y = 10 into the first equation to get the value of x

x = 25 – y = 25 – 10 = 15

The two numbers are 15 and 10.

Is it right or not? Check it out!

15 + 10 = 25

15² – 10² = 225 – 100 = 125

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 sum and difference of squares. The calculator omits all steps and displays the answer in milliseconds.

Next, we will introduce how to use the calculator.

Using the calculator is simple, follow these 3 steps:

Next, let’s look at some examples.