SOLUTION: Please note that ----------- ------ represents division The unknown variables x,y,z satisfy the equations {{{x+y}}} {{{1-z-z^2}}} --------- == ----------- ---- {{{1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please note that ----------- ------ represents division The unknown variables x,y,z satisfy the equations {{{x+y}}} {{{1-z-z^2}}} --------- == ----------- ---- {{{1      Log On


   

Question 889193: Please note that ------------------ represents division
The unknown variables x,y,z satisfy the equations

x%2By 1-z-z%5E2
--------- == ----------------
1%2Bz. x%5E2-xy%2By%5E2
x-y. 9%2B3z%2Bz%5E2
--------- == ----------------
3-z. x%5E2%2Bxy%2By%5E2
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Unfortunately, you didn't give any instructions.

There are three variables with only 2 equations.

There are probably infinitely many solutions.

I will assume the instructions were:

Find the real value of x, 

I will also assume the sign of z%5E2 should have been 
positive in the first equation, not negative.   Otherwise, 
we cannot have a unique solution for any of the three letters. 

Then the system is
 


Cross multiply:



Multiply those out:

system%28x%5E3%2By%5E3=1%2Bz%5E3%2Cx%5E3-y%5E3=27-z%5E3%29

Add the 2 equations and you get 

2x%5E3=28

x%5E3=14

x=root%283%2C14%29

Sorry if that's not what you were asked to do.

There is no way for us to tell what the instructions 
could be since there are more unknowns than equations.

Edwin