Find 2 Numbers by Sum of Squares and Difference of Squares Calculator

Welcome to the free online calculator to find two numbers by a given sum of squares and the difference of squares. For example, the sum of the squares of two numbers is 225, and the difference of their squares is 63. What are the two numbers?

Let the two numbers be x and y.

According to the question, we can get two equations

x² + y² = 225………(1)

x² – y² = 63………(2)

Add the first equation to the second equation

(x² + y²) + (x² – y²) = 225 + 63

x² + y² + x² – y² = 288

2x² = 288

x² = 144

x = 12 or x = -12

Substitute the value of x into the first equation to calculate the value of y.

x² + y² = 225

144 + y² = 225

y² = 81

y = 9 or y = -9

Note that instead of two, 4 sets of numbers can be formed based on the values of x and y.

(12, 9), (12, -9), (-12, 9), (-12, -9)

Let’s verify.

12² + 9² = 144 + 81 = 225

12² – 9² = 144 – 81 = 63

Or

12² + (-9)² = 144 + 81 = 225

12² – (-9)² = 144 – 81 = 63

Or

(-12)² + 9² = 144 + 81 = 225

(-12)² – 9² = 144 – 81 = 63

Or

(-12)² + (-9)² = 144 + 81 = 225

(-12)² – (-9)² = 144 – 81 = 63

Correct.

Very simple. The key is to calculate the square root. If you are not familiar with this, it is recommended to use the free calculator available on this page to find two numbers by the sum of squares and the difference of squares.

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.