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

Respuesta :

Answer:

The product of the integers is the sum of the products of two different integers , i.e xyz = xy + yz + zx   .

Step-by-step explanation:

Given as :

The sum of the reciprocals of three different integers $1

Let The three different integers are x , y , z

So, The reciprocals of integers = [tex]\dfrac{1}{x}[/tex] , [tex]\dfrac{1}{y}[/tex] ,[tex]\dfrac{1}{z}[/tex]

Now, According to question

∵ The sum of the reciprocals of three different integers = $1

Or, [tex]\dfrac{1}{x}[/tex] + [tex]\dfrac{1}{y}[/tex] + [tex]\dfrac{1}{z}[/tex] = $1

Now, Taking LCM

I.e [tex]\dfrac{xy + yz + zx}{xyz}[/tex] = $1

Or, xyz = xy + yz + zx

So, The product of the integers = The sum of the products of two different integers

Hence, The product of the integers is the sum of the products of two different integers , i.e xyz = xy + yz + zx   . Answer

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