Finding the Difference of the Cubes of Two NumbersDate: 9/29/95 at 21:57:3 From: Anonymous Subject: Solve for x^3 - y^3 Here's the problem : The difference of two numbers is 1. The product of the two numbers is also 1. What is the difference of the cubes of the numbers? Date: 9/30/95 at 1:52:37 From: Doctor Andrew Subject: Re: Solve for x^3 - y^3 Let x be the bigger number and y be the smaller. Then we know that x - y = 1. We also know that x * y = 1 So we know two things: x - y = 1 x * y = 1 If you want to solve this algebraically, pick one of these equations and use it to solve for either x or y in terms of the other variable (y or x, respectively). Then substitute that expression for x or y into the equation you didn't use. You will get a quadratic expression (that means you'll have a term raised to the second power) so you can use the quadratic formula to solve it. If you're not familiar with the quadratic formula, you can read about it here: http://mathforum.org/library/drmath/view/53198.html Once you've found values for x and y, you can cube them and subtract to get the difference. -Doctor Andrew, The Geometry Forum Date: 9/30/95 at 14:54:47 From: Doctor Ken Subject: Re: Solve for x^3 - y^3 Hello! Let me offer another way you could approach this problem. I'll give you an example of a different but similar problem: x - y = 2 xy = 7 What is x^2 + y^2? Well, since x-y = 2, squaring both sides gives x^2 - 2xy + y^2 = 4. Since xy = 7, we can add 2xy to both sides (it will get rid of the middle term on the left, and add 14 on the right). That gives us x^2 + y^2 = 18. Now do you see how you could do your problem? -Doctor Ken, The Geometry Forum |
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