Find 2 Numbers by Difference and Difference of Cubes Calculator

Welcome to the free online calculator to find two numbers by given difference and difference of cubes. For example, the difference of two numbers is 4 and the difference of their cubes is 316. 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 = 4………(1)

x³ – y³ = 316………(2)

Cube both sides of the first equation and simplify to get the third equation.

(x – y)³ = 4³

x³ – 3x²y + 3xy² – y³ = 64

x³ – y³ – 3xy(x – y) = 64………(3)

Substitute the first and second equations into the third equation to get the 4th equation,

316 – 3xy * 4 = 64

12xy = 252

xy = 21………(4)

Based on Equation 1 and Equation 4, the problem becomes that the difference of two numbers is 4 and their product is 21. What are the numbers? How to solve it? There are 2 methods, one is the quadratic equation method and the other is the factor method. For the specific process, please refer to the calculator finds two numbers by difference and product.

Here, the quadratic equation method is used to solve.

Since x – y = 4, so x = 4 + y. Put this value into the 4th equation.

(4 + y)y = 21

4y + y² = 21

y² + 4y – 21 = 0

(y + 7) (y – 3) = 0

Y = -7 or y = 3

From the relationship between x and y, we can easily calculate the value of x.

x = -3 or x = 7

So, the two numbers are (-3, -7) or (7, 3).

Let’s verify.

(-3) – (-7) = 4

(-3)³ – (-7)³ = -27 + 343 = 316

Or

7 – 3 = 4

7³ – 3³ = 343 – 27 = 316

The answer is correct.

Obviously, it is not simple to find two numbers based on the difference and the difference of cubes by hand. So, we developed this free online calculator to find two numbers by the difference and difference of cubes. 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.