Find 2 Numbers by Difference and Reciprocal Calculator

Welcome to the free online calculator to find two numbers by given difference and reciprocal. For example, the difference of two numbers is 4, and the difference of their reciprocal is 18. What are the two numbers?

Let the two numbers be x and y.

According to the question, we can get two equations

x – y = 4………(1)

1y – 1x = 18………(2)

Simplify the second equation.

1y – 1x = 18

x – yxy = 18………(3)

Substitute the first equation into the third equation and simplify.

x – yxy = 18

4xy = 18

xy = 32………(4)

Based on Equation 1 and Equation 4 the problem becomes that the difference of two numbers is 4 and their product is 32. What are the two numbers? Go to Find Two Numbers by Difference and Product Calculator for details.

Because x – y = 4, so x = 4 + y. Substitute this value into the 4th equation.

xy = 32

(4 + y)y = 32

4y + y² = 32

y² + 4y – 32 = 0

(y – 4) (y + 8) = 0

y = 4 or y = -8

According to the relationship between x and y, we can calculate the value of x.

x = 4 + y = 4 + 4 = 8

or

x = 4 + y = 4 + (-8) = -4

So, the two numbers are (8, 4) or (-4, -8).

Verify.

8 – 4 = 4

14 – 18 = 2 – 18 = 18

Or

-4 – (-8) = 4

1-8 – 1-4 = 14 – 18 = 2 – 18 = 18

Correct.

The whole process is not difficult, the key is the solution of the quadratic equation. If you don’t want to calculate, it is recommended to use the free calculator available on this page to find two numbers by the difference and reciprocal. 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.