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?
2 answers:
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 .
If the three integers are , then we have
We can combine the fractions on the left side:
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