Chapter 11: Q. 75 (page 774)

The difference of two numbers is the same as their product, and the sum of their reciprocals is $5$ . Find the numbers.

Short Answer

Expert verified

The two numbers are $\frac{1}{2} a n d \frac{1}{3}$ .

Step by step solution

Step 1. Given information.

Assume the two numbers to be xand y.

From the question,

$x - y = x y . . . . . . (i) \frac{1}{x} + \frac{1}{y} = 5 . . . . . . (i i)$

Multiply equation (ii) with xy,

role="math" localid="1646838166713" $\frac{x y}{x} + \frac{x y}{y} = 5 x y y + x = 5 x y . . . . . . (i i i)$

Step 2. Find the two numbers.

Add equations (i) and (iii),

$(x + y) + (x - y) = 5 x y + x y 2 x = 6 x y y = \frac{1}{3}$

Substitute the value ofy equation (i),

$x - \frac{1}{3} = \frac{x}{3} x - \frac{x}{3} = \frac{1}{3} \frac{2 x}{3} = \frac{1}{3} x = \frac{1}{2}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

The difference of two numbers is the same as their product, and the sum of their reciprocals is $5$ . Find the numbers.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the two numbers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Theoretical and Mathematical Physics

Geometry

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

The difference of two numbers is the same as their product, and the sum of their reciprocals is 5. Find the numbers.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the two numbers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Theoretical and Mathematical Physics

Geometry

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

The difference of two numbers is the same as their product, and the sum of their reciprocals is $5$ . Find the numbers.