Find Two Numbers by Sum and Reciprocal Calculator

Welcome to the free online calculator to find two numbers by given sum and reciprocal. For example, the sum of two numbers is 100, and the sum of their reciprocal is 4/51. What are the two numbers?

Let the two numbers be x and y.

According to the question, we can get two equations

x + y = 100………(1)

1x + 1y = 451………(2)

Simplify the second equation.

1x + 1y = 451

x + yxy= 451………(3)

Substitute the first equation into the third equation and simplify.

x + yxy= 451

100xy= 451

xy = 1275………(4)

Based on Equation 1 and Equation 4 the problem becomes that the sum of two numbers is 100 and their product is 1275. What are the two numbers? Go to Find Two Numbers by Sum and Product Calculator for details.

Because x + y = 100, so x = 100 – y. Substitute this value into the 4th equation.

xy = 1275

(100 – y) y = 1275

100y – y² = 1275

y² – 100y + 1275 = 0

(y -15) (y – 85) = 0

y = 15 or y = 85

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

x = 100 – y = 100 – 15 = 85

or

x = 100 – y = 100 – 85 = 15

So, the two numbers are 15 and 85.

Verify.

15 + 85 = 100

115 + 185 = 85 + 1515 * 85 = 1001275 = 451

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 sum 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.