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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 12and13.

Step by step solution

01

Step 1. Given information.

Assume the two numbers to be xand y.

From the question,

x-y=xy......(i)1x+1y=5......(ii)

Multiply equation (ii) with xy,

role="math" localid="1646838166713" xyx+xyy=5xyy+x=5xy......(iii)

02

Step 2. Find the two numbers.

Add equations (i) and (iii),

x+y+x-y=5xy+xy2x=6xyy=13

Substitute the value ofy equation (i),

x-13=x3x-x3=132x3=13x=12

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Most popular questions from this chapter

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

x=2y;x=y2-2y

Verify that the values of the variables listed are solutions of the system of equations.

4x-z=78x+5y-z=0-x-y+5z=6x=2,y=-3,z=1;2,-3,1

Verify that the values of the variables listed are solutions of the system of equations.

4x-5z=65y-z=-17-x-6y+5z=24x=4,y=-3,z=2;4,-3,2

Graph each equation of the system. Then solve the system to find the points of intersection.

y=x2+1y=x+1

solve each system of equations. If the system has no solution, say that it is inconsistent.

x + y - z = 6

3x - 2y + z = -5

x + 3y - 2z = 14
See all solutions

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