Equal Sum, Product, Quotient of Two NumbersDate: 10/13/2002 at 20:20:38 From: Liz Ureste Subject: Math problem I need to know the sum, product, and quotient of two different numbers that are all equal. What are the two numbers? I don't know how to start the problem. Date: 10/13/2002 at 22:20:54 From: Doctor Ian Subject: Re: Math problem Hi Liz, Well, if we call the numbers x and y, then we know that the following must be true: x + y = x * y x + y = x / y x * y = x / y What we really want to do is get one of these variables (x or y) by itself on one side of an equation, because then we can substitute for it in another equation. Let's look at the third equation: x * y = x / y x * y * y = x y * y = x / x y^2 = 1 y = 1 or -1 That narrows things down considerably. Now let's look at the first equation. Since y must be 1 or -1, one of the following must be true: 1) x + 1 = x * 1 2) x - 1 = x * -1 The first one can't be true for any number, since one operation changes the value of x and the other doesn't. But what about the second equation? Can you find a number that makes it true? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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