Numbers question?

[luvmykids911]

Hello. I am Martha Byrd, I am helping my child do a problem. I myslfe have not taken algebra for quite a few years now. Can someone help me understand this problem? Thanks.

Martha

Problem reads:

Find two numbers such that their differenceis 1 and their product is 1. (Let x be the larger number and y the smaller number.)

* See I am not sure how to set this up or what formula to use. ANy help is greatly appreciated. Thanks again in advance!

 

[Gene]

Find two numbers such that their difference is 1 and their product is 1. (Let x be the larger number and y the smaller number.)

Find two numbers such that y-x=1 and y*x = 1. (Let x be the larger number and y the smaller number.)
y-x=1
y=x+1

y*x = 1
(x+1)*x=1
x^2+x-1=0
What you do with that depends on what you know.
The quadratic equation seems indicated.

 

[soroban]

Hello, Martha!

Find two numbers such that their difference is 1 and their product is 1.
(Let x be the larger number and y the smaller number.)

Evidently, your child is expected to be familiar with "system of equations".

They suggested: let \(\displaystyle x\) = larger number, \(\displaystyle y\) = smaller number.

"Their difference is 1." . (Baby-talk: when you subtract them, you get 1.]
. . So we can write: .\(\displaystyle x\,-\,y\:=\:1\) .[1]

"Their product is 1." . [Baby-talk: when you multiply them, you get 1.]
. . So we can write: .\(\displaystyle xy \:=\:1\) .[2]

We must solve this system:
. . . [1] \(\displaystyle x\,-\,y\:=\:1\)
. . . [2] . \(\displaystyle xy\;\;=\;1\)

From [1] we get: .\(\displaystyle x\:=\:y\,+\,1\) .[3]

Substitute into [2]: .\(\displaystyle (y\,+\,1)y\:=\:1\)

. . and we get the qudratic equation: .\(\displaystyle y^2\,+\,y\,-\, 1\:=\:0\)

Using the Quadratic Formula, we get: .\(\displaystyle \L y\:=\:\frac{-1\,\pm\,\sqrt{5}}{2}\)

Using [3] we get: .\(\displaystyle \L x\;=\;\frac{1\,\pm\,\sqrt{5}}{2}\)


Edit: Too fast for me, Gene!

 

[Gene]

Soroban saves everyone from thinking too much and types prettier equations than I do. :twisted:

 

[luvmykids911]

Thank you guys. So that is the answer and that is how you do the problem?

 

[stapel]

So that is the answer and that is how you do the problem?

When Gene joked that you don't have to think now, you only have to copy this into the homework, that may safely be taken to mean that "this is the answer and this is how you do it".

Eliz.

 

[maxboy0801]

Hey guys, I was trying to do this problem and I am confused. I thought I could help her but now I am just puzzled and I want some closure. What are the 2 numbers?

Max

 

[stapel]

What are the 2 numbers?

Are you not able to see Soroban's complete worked solution (above)? Is the text not displaying or something?

Eliz.