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September 18th, 2019, 02:17 PM   #1
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Please help solve the equations

Please help solve the equations
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September 18th, 2019, 02:27 PM   #2
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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.
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September 18th, 2019, 03:35 PM   #3
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I think they means solve all 3 simultaneously.
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September 18th, 2019, 03:39 PM   #4
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Mathematica has exact solutions but they are rather lengthy.

Here are the numerical approximations

$\{x,y,z\} =
\left(
\begin{array}{ccc}
-0.215425+0.264713 i & -0.215425-0.264713 i & 1.43085 \\
-0.215425+0.264713 i & 1.43085 & -0.215425-0.264713 i \\
-0.215425-0.264713 i & -0.215425+0.264713 i & 1.43085 \\
-0.215425-0.264713 i & 1.43085 & -0.215425+0.264713 i \\
1.43085 & -0.215425-0.264713 i & -0.215425+0.264713 i \\
1.43085 & -0.215425+0.264713 i & -0.215425-0.264713 i \\
\end{array}
\right)$
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