Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

The sum of two numbers is the same as their product, and the difference of their reciprocals is $3$ . Find the numbers.

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Assume the two numbers to be x and y.

From the question,

$x + y = x y . . . . . . (i) \frac{1}{x} - \frac{1}{y} = 3 . . . . . . (i i)$

Multiply equation (ii) with xy,

role="math" localid="1646841503959" $\frac{x y}{x} - \frac{x y}{y} = 3 x y y - x = 3 x y . . . . . . (i i i)$

Step 2. Find the two numbers.

Add equations (i) and (iii),

$(x + y) + (y - x) = x y + 3 x y 2 y = 4 x y x = \frac{1}{2}$

Substitute the value of y equation (i),

$\frac{1}{2} + y = \frac{1}{2} y y - \frac{y}{2} = - \frac{1}{2} y = - 1$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

The sum of two numbers is the same as their product, and the difference of their reciprocals is $3$ . Find the numbers.

Step by Step Solution

Step 1. Given information.

Step 2. Find the two numbers.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

The sum of two numbers is the same as their product, and the difference of their reciprocals is 3. Find the numbers.

Step by Step Solution

Step 1. Given information.

Step 2. Find the two numbers.

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The sum of two numbers is the same as their product, and the difference of their reciprocals is $3$ . Find the numbers.