# A Mathematical Queiz

February 9, 2010 4 Comments

There are two numbers, the difference between them is two. Their multiplication equal their sum plus fourteen?

A similar questions was asked few days ago on facebook between teenagers. One of teenagers did not know the answer (or maybe the question). The other was able to answer it in few minutes. The time taken to answer the question was impressive. They might had help from an adult or a calculator but at least they have the motivation to answer it.

This questions represent a hyperbola and can be mathematically represented by:

*xy = (x + y) + 14*

*y – x = 2*

that can be reduced to

** y = (x + 14) / (x – 1)** where

*x – 1 ≠ 0*Hyperbola according to WolframAlfa definition is an open curve formed by a plane that cuts the base of a right circular cone. So to reach the desired answer for the question you may replace an integer in place of x and calculate the result. You should start by the number 2 because **x -1 ≠ 0**. You will reach the result when you set ** x = 4 **and then

**will equal 6.**

*y*
You have forgotten to mention the second part of the equation (y-x=2). It is shown in the graph. Likes it

Many thanks for spotting that mistake. Necessary correction is done.

What about the other part of the solution.

This equation is a second order equation and should have two solutions.

xy=x+y+14

y-x=2

==> x=y-2

==> y2 – 2y = 2y – 2 + 14

==> y2 – 4y – 12 = 0

(y-6)(y+2)=0 ==> y = 6 or -2

==> x = 4 or -4 respectively

modawanah.wordpress.com

You are right the other possible answer is: x = -4, y = -2 thank you for sharing that with us.