
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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February 20th, 2018, 12:44 PM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 238 Thanks: 27  System equation
Solve the system $\displaystyle x^2 + x 1=y$ $\displaystyle y^2 +y1=z$ $\displaystyle z^2 +z1=x$ 
February 20th, 2018, 12:53 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,767 Thanks: 1422 
sum of the three equations ... $x^2+y^2+z^2 + x + y + z  3 = y+z+x$ $x^2+y^2+z^2 = 3$ sphere of radius $r=\sqrt{3}$ centered at the origin ... https://www.wolframalpha.com/input/?...E2%2Bz%5E2%3D3 
February 20th, 2018, 01:15 PM  #3  
Global Moderator Joined: May 2007 Posts: 6,581 Thanks: 610  Quote:
 
February 20th, 2018, 02:21 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,505 Thanks: 1741 
If the solutions don't have to be real, there are more solutions.

February 20th, 2018, 02:56 PM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 2,090 Thanks: 1086 
it ends up being the roots of a degree 6 polynomial

February 20th, 2018, 07:26 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,505 Thanks: 1741 
If $x$ isn't real, it's a zero of $x^6 + 4x^5 + 5x^4 + 2x^3 + 1$.


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