September 6th, 2018, 02:55 PM  #1 
Newbie Joined: Sep 2018 From: Spain Posts: 4 Thanks: 0  Solve this system of equations
x^2+yz+y^2*x=0 y^2+xz+z^2*y=0 z^2+xy+x^2*z=0 
September 6th, 2018, 04:45 PM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 504 Thanks: 283 Math Focus: Dynamical systems, analytic function theory, numerics 
Ok. Done.

September 6th, 2018, 04:54 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,489 Thanks: 950 
Hmmmm....a=0, b=0, c=0 Ahem!! 
September 6th, 2018, 05:15 PM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,175 Thanks: 1143 
there is another real solution as well

September 6th, 2018, 05:18 PM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,489 Thanks: 950  
September 6th, 2018, 08:11 PM  #6 
Senior Member Joined: Sep 2015 From: USA Posts: 2,175 Thanks: 1143  
September 6th, 2018, 09:42 PM  #7 
Newbie Joined: Sep 2018 From: Spain Posts: 4 Thanks: 0 
Thank you guys, though I guess, I didn't make myself clear enough. I meant: determine all real solutions and, having done so, prove that there are no other real solutions.
Last edited by Jungle12; September 6th, 2018 at 10:03 PM. 
September 7th, 2018, 04:54 AM  #8 
Senior Member Joined: Sep 2016 From: USA Posts: 504 Thanks: 283 Math Focus: Dynamical systems, analytic function theory, numerics 
This is how you find them: https://en.wikipedia.org/wiki/Newton%27s_method This is how you prove there aren't any others: 6.4.2 Cylindrical Algebraic Decomposition 
September 7th, 2018, 04:59 AM  #9 
Global Moderator Joined: Dec 2006 Posts: 19,888 Thanks: 1836  
September 7th, 2018, 07:34 AM  #10 
Newbie Joined: Sep 2018 From: Spain Posts: 4 Thanks: 0 
A mate of mine asked me to solve it for them, I wasn't able to, so I asked for it here 

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algebra, equations, inequality, solve, system 
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