# smallest of 3 integers

The sum of the reciprocals of three consecutive positive integers is equal to 47 divided by the product of the integers. What is the smallest of the three integers?

1. 👍 0
2. 👎 0
3. 👁 690
1. 1/(x-1) + 1/x + 1/(x+1) = 47/[(x-1)x(x+1)]
put all over a common denominator of (x-1)x(x+1). The numerators then satisfy

x(x+1) + (x-1)(x+1) + (x-1)x = 47
3x^2 - 1 = 47
3x^2 = 48
x = 4

check:
1/3 + 1/4 + 1/5 = 47/60

1. 👍 0
2. 👎 1

## Similar Questions

1. ### Math

If the product of 4 consecutive integers is equal to one of the integers, what is the largest possible value of one of the integers? The answer is 3, but I do not understand how it is 3. I tried writing out 4 consecutive #'s such

2. ### math

the sum of two consecutive even integers is at most seven more than half the sum of the next two consecutive even integers

3. ### math induction

prove the product of 4 consecutive integers is always divisible by 24 using the principles of math induction. Could anyone help me on this one? Thanks in advance! Sure For induction we want to prove some statement P for all the

4. ### Math

The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!

1. ### Math

The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking

2. ### Math

2. The sum of the reciprocals of two consecutive positive integers is 17/72. Write an equation that can be used to find the two integers. What are the integers? Steve helped me yesterday and gave me the hint 8+9=17. Then I thought

3. ### Algebra 2

The sum of the reciprocals of two consecutive even integers is 9/40. this can be represented by the equation shown. (1/x)+(1/x+2)=9/40 Use the rational equation to determine the integers. Please help!! I have no idea what to do:(

4. ### Math

The sum of two consecutive numbers divided by their positive difference is equal to 9. Find the largest number.

1. ### algebra

Five times the smallest of three consecutive odd integers is ten more than twice the longest. Find the integers. The sum of three integers is one hundred twenty three more than the first number. The second number is two more than

2. ### math

the sum of the square of two consecutive positive integers is 265.what are the integers?

3. ### Mathmatics

Prove algebraically that the difference between the square of any two consecutive integers is equal to the sum of these two integers. First number = n Second number = n+1 Square the second number: (?????)^2 Difference between the

4. ### Math

If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?