1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Charra [1.4K]
3 years ago
15

Melissa has three different positive integers. She adds their reciprocals together and gets a sum of $1$. What is the product of

her integers? Melissa has three different positive integers. She adds their reciprocals together and gets a sum of $1$. What is the product of her integers?
Mathematics
2 answers:
ryzh [129]3 years ago
6 0

Answer:

36

Step-by-step explanation:

Let the three positive integers be x, y, and z. Then

1/x + 1/y + 1/z = 1

Assume x = 2.

Then 1/x = ½ and 1/y + 1/x = 1/2

Divide the second portion (1/y + 1/z) into three parts.

3/6 = 1/6 + (1/6 +1/6)

Combine two of the fractions.

1/2 = 1/6 + 2/6

1/2 = 1/6 + 1/3

1/2 + 1/3 + 1/6 = 1

The integers are 2, 3, and 6.

2 × 3 × 6 = 36

The product of Melissa’s integers is 36.

Whitepunk [10]3 years ago
4 0

If the three integers are a,b,c, then we have

\dfrac1a+\dfrac1b+\dfrac1c=1

We can combine the fractions on the left side:

\dfrac{bc}{abc}+\dfrac{ac}{abc}+\dfrac{ab}{abc}=\dfrac{bc+ac+ab}{abc}=1

\implies abc=bc+ac+ab

You might be interested in
Evaluate the following, if a=7, b=3, c=2
Zinaida [17]

Answer:

Step-by-step explanation:

a^2 - 5bc - 1

a = 7

b = 3

c = 2

7^2 - 5*3*2 - 1

49 - 30 - 1

18

4 0
2 years ago
Compute $\sqrt{25^2-7^2}$.
EastWind [94]

Answer:

24

Step-by-step explanation:

\sqrt{25^2-7^2}\\\\=\sqrt{(25-7)(25+7)}\\\\=\sqrt{18(32)}\\\\=\sqrt{9*2*2^5}\\\\=\sqrt{3^2\cdot 2^6}\\\\=\sqrt{(3\cdot2^3)^2}\\\\=3\cdot2^3\\\\=3\cdot8\\\\=24

5 0
3 years ago
8(9/5)-2= what?<br> 3(9/5)+7=what?
mario62 [17]
12.4 is the answer for both
3 0
3 years ago
(NEED HELP ASAP! PICTURE IS PROVIDED WITH THE QUESTION.)
yuradex [85]

Answer:

i cant see picture

Step-by-step explanation:

7 0
2 years ago
Solve the Absolute Value Equation. <br><br> |9x+1| = 46
Sedaia [141]
X = 5 (you can set it up as a regular equation)
9x + 1= 46
9x = 45 (subtracted 1 from both sides)
x = 5 (divided 45 by 9)
hope this helps :)
5 0
3 years ago
Other questions:
  • What is the surface area of a sphere with a radius of 6 m rounded to the nearest square meter?
    15·1 answer
  • What is the standard form of 3^5​
    5·1 answer
  • Find the function rule.<br> x –2 –1 0 1 2<br> y 9 4 –1 –6 –11
    14·1 answer
  • HELP PLEASE ASAP!!!!
    7·1 answer
  • During the 2004 senatorial campaign in a large southwestern state, illegal immigration was a major issue. One of the candidates
    13·1 answer
  • Helpppp anyoneee plssss
    9·1 answer
  • SImplify:<br><br> (2m)^5<br><br> Please help if possible :)
    12·2 answers
  • Bettie’s Boutique is having a $$ off sale.
    15·1 answer
  • Suppose you know the slope of a linear relationship and one of the points that it's graphed passes through. How can you determin
    6·1 answer
  • A bowl has only red, green, and purple grapes. The probability of picking a red grape out of the bowl, eating it, and then picki
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!