Unique Values for x, yDate: 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/ |
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