Research LInks

Find the solution for the system of equations:

        X+YZ=6            Y+XZ=6             Z+XY=6  

Multiply each equation by the term missing to make each second term a triple

 X^2+XYZ=6X             Y^2+XYZ=6Y             Z^2+XYZ=6Z  

So now subtract the second equation from the first: 

 X^2 -Y^2=6(X-Y)    

(X+Y)(X -Y)=6(X-Y)    


Since the equations are symmetric we should have

(X+Y)=6        (X+Z)=6           (Y+Z)=6 

Subtracting the 3rd from the 1st:

X - Z =0   or 

 X = Z     and again since the equations are symmetric  X = Y = Z  


The very first equation at the top  X+YZ=6   becomes

 X^2+X - 6=0  

 X^2+X - 6=0  

 (X+3)(X-2)=0   giving the solutions

 X = 2,-3 

Categories: Math

Fudgy McFarlen

Woo hoo.

Leave a Reply

Your email address will not be published. Required fields are marked *

Related Posts

Jordan Peterson

Jordan Peterson on Prices Law

Price’s Law says that 50% of work at a company is done by the square root of the number of employees.  As an example take a company with 100 employees.  In that company 10 people Read more…


Reason for using Base 60 or 360 for Angles

Babylonian Triangle Table Research Links Wikipedia: Plimpton 322 Tablet Forget trigonometry, 'cos Babylonians did it better 3,700 years ago – by counting in base 60! Ancient Babylonian use of the Pythagorean Theorem and its Three Read more…


The Inevitable Knot in Your Long Extension Cord

This knot in my extension cord occurred inadvertently and thus I assumed with the highest likelihood it could be undone with a single pass through a cable end through a loop or loops with the loops Read more…