Equation solving problem

• To: mathgroup at smc.vnet.net
• Subject: [mg125042] Equation solving problem
• From: Juhász Péter <juhaszp.piarhf at gmail.com>
• Date: Sun, 19 Feb 2012 06:31:08 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```I have the following problem: I would like to solve a set of 3
equations, but Mathematica's solution involves unknown variables. My
input was:

Solve[{nc^2/Sqrt[1 - v^2/c^2] == mc^2/Sqrt[1 - b^2/c^2] + pc,
nv/Sqrt[1 - v^2/c^2] == (mb Cos[\[Alpha]])/Sqrt[1 - b^2/c^2] +
p Sin[\[Alpha]], (mb Sin[\[Alpha]])/Sqrt[1 - b^2/c^2] ==
p Cos[\[Alpha]]}, {v, b, p}]

And the output started like:

{{v -> -(I c \[Sqrt](mc^4 nv^2 Cos[\[Alpha]]^2 -
2 mb mc^2 nc^2 nv Cos[\[Alpha]]^3 +
mb^2 nc^4 Cos[\[Alpha]]^4 - mb^2 pc^2 Cos[\[Alpha]]^4 -
2 mb mc^2 nc^2 nv Cos[\[Alpha]] Sin[\[Alpha]]^2 +
2 mb^2 nc^4 Cos[\[Alpha]]^2 Sin[\[Alpha]]^2 -
2 mb^2 pc^2 Cos[\[Alpha]]^2 Sin[\[Alpha]]^2 +
mb^2 nc^4 Sin[\[Alpha]]^4 -
mb^2 pc^2 Sin[\[Alpha]]^4))/(mb pc Sqrt[
Cos[\[Alpha]]^4 + 2 Cos[\[Alpha]]^2 Sin[\[Alpha]]^2 +
Sin[\[Alpha]]^4]),
b -> -1/(nv pc) (\[Sqrt](-c^2 mc^4 nv^2 + c^2 nv^2 pc^2 +
2 c^2 mb mc^2 nc^2 nv Cos[\[Alpha]] -
c^2 mb^2 nc^4 Cos[\[Alpha]]^2 -
2 c^2 mb^2 nc^4 Sin[\[Alpha]]^2 +
2 c^2 mb mc^2 nc^2 nv Sin[\[Alpha]] Tan[\[Alpha]] -
c^2 mb^2 nc^4 Sin[\[Alpha]]^2 Tan[\[Alpha]]^2)),
.... .... ....

And so on. It is clear, that if we look at the solution for v, it
involves unknowns b and p. If anyone could tell me what I did wrong, I
would highly appreciate it.