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September 18th, 2019, 02:17 PM  #1 
Newbie Joined: Sep 2019 From: Ksa Posts: 1 Thanks: 0  Please help solve the equations
Please help solve the equations

September 18th, 2019, 02:27 PM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 310 Thanks: 162 
What do you mean by "solve the equations?" Those equations describe surfaces in three dimensions (if x, y, and z are your coordinates). They are a plane, a sphere, and... I don't even know what you would call the third one. Every single point on the surface is a solution to the corresponding equation. 
September 18th, 2019, 03:35 PM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,588 Thanks: 1432 
I think they means solve all 3 simultaneously.

September 18th, 2019, 03:39 PM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,588 Thanks: 1432 
Mathematica has exact solutions but they are rather lengthy. Here are the numerical approximations $\{x,y,z\} = \left( \begin{array}{ccc} 0.215425+0.264713 i & 0.2154250.264713 i & 1.43085 \\ 0.215425+0.264713 i & 1.43085 & 0.2154250.264713 i \\ 0.2154250.264713 i & 0.215425+0.264713 i & 1.43085 \\ 0.2154250.264713 i & 1.43085 & 0.215425+0.264713 i \\ 1.43085 & 0.2154250.264713 i & 0.215425+0.264713 i \\ 1.43085 & 0.215425+0.264713 i & 0.2154250.264713 i \\ \end{array} \right)$ 

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