Unique Values for x, y

Date: 9/10/96 at 16:46:45
From: Anonymous
Subject: Values for x, y Such That...

What are unique values for x and y so that x+y and y*x equal the 
same number?

Thanks.

Date: 9/10/96 at 19:56:40
From: Doctor Mike
Subject: Re: Values for x, y Such That...

Hello, 
  
I can think of 2 solutions quickly, namely X = 0, Y = 0 and 
X = 2, Y = 2. 

Are you looking for solutions with different values for X and Y?   
You could take X = 3 and Y = 3/2 .  There are many other solutions.  
If you are curious how I know that, read on. 
  
In order for X+Y and X*Y to equal the same number they have to equal 
each other, so you have the equation X*Y=X+Y. You can solve for Y in 
terms of X to better understand this. The first step is to subtract 
Y from both sides to get X*Y-Y=X. The next step is to factor the left 
side to get (X-1)*Y=X. Then divide both sides by (X-1) to get 
Y=X/(X-1).  This says you can select almost any value for X, and the 
formula will give you a Y that works with that X. The only forbidden 
X value is one (1), which makes the denominator zero.  

A solution that is a little farther out is Y=1.01 and X=101.
If you know about graphing equations, this is an interesting one!
  
I hope this helps.  
  
-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/