Sum of numbers is 2, product is 3; find sum of reciprocals

[lisaz0224]

Hi people, I'm in a sixth grade class and I just got this question. Can you please help me?

The sum of two numbers is 2, the product of the same two numbers is 3. What is the sum of the reciprocals of the two numbers?

Thanks! Please tell me how you got the answer, not just some random fraction.

 

[Mrspi]

Re: Please Help, I think it's impossible

Hi people, I'm in a sixth grade class and I just got this question. Can you please help me?
The sum of two numbers is 2, the product of the same two numbers is 3. What is the sum of the reciprocals of the two numbers?
Thanks!
Please tell me how you got the answer, not just some random fraction.

Let x = the first number, and
let y = the second number


The sum of the two numbers is 2. So,
x + y = 2

The product of the two numbers 3....so,
xy = 3

Now...you are looking for the sum of the reciprocals of the two numbers. So, you're looking for the value of

(1/x) + (1/y)

Simplify the sum of the two fractions. (1/x) can be written as (y/xy). (1/y) can be written as (x/xy).

(1/x) + (1/y) = (y/xy) + (x/xy)

Add the two fractions...they have the same denominator, so you can add the numerators, and put the result over the common denominator:

(y/xy) + (x/xy) = (y + x) / (xy)

LOOK at what is given. What is x + y? What is xy?

Can you finish it now? If not, please repost showing ALL of the work you've done.

 

[lisaz0224]

Re: Please Help, I think it's impossible

woah... I see. You don't even have to find the values of x and y. At the end, when you get back to the original equations, you get 2/3. If I did it correctly. Thanks so much!!

 

[Mrspi]

Re: Please Help, I think it's impossible

woah... I see. You don't even have to find the values of x and y. At the end, when you get back to the original equations, you get 2/3. If I did it correctly. Thanks so much!!

Right!!

 

[leooo]

sorry but i still dont get it

Right!!

So understand how it turns to x+y/xy but dont understand how all ofa sudden it is 2/3
I got stuck on ths question as well, please explain the last part thank you

 

[mmm4444bot]

So understand how it turns to (x+y)/(xy) but dont understand how all ofa sudden it is 2/3
I got stuck on ths question as well, please explain the last part thank you

Before I answer your question, please look at the red grouping symbols above. When we write an algebraic fraction on paper, we simply write x+y on top and xy on bottom (because we can draw a fraction bar to separate them). However, when we TYPE such a fraction, we cannot draw a fraction bar. Instead, we need to type grouping symbols around the numerator and denominator, to clearly show what's on top and what's on bottom, like this:

(x+y)/(xy)

Without those grouping symbols, your typing means something else (due to Order of Operations).

---

Okay. You're asking how we know that x+y=2 and x*y=3.

:idea: Remember what the symbols x and y represent.

x and y represent the two unknown numbers, in this exercise.

We're told that their sum is 2. That means x+y is 2.

We're told that their product is 3. That means x*y=3.

It's this given information that allows us to substitute the number 2 for the expression x+y and to substitute the number 3 for the expression x*y. :cool: