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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

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6 0
3 years ago
Read 2 more answers
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nignag [31]

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Step-by-step explanation:

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7 0
2 years ago
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3 years ago
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strojnjashka [21]
The mean book rating will decrease

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divide the total with the total amount of numbers

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5 0
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