Re: solved in a non algebraic way?
- To: mathgroup at smc.vnet.net
- Subject: [mg42219] Re: [mg42189] solved in a non algebraic way?
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Tue, 24 Jun 2003 01:27:05 -0400 (EDT)
- References: <200306220057.UAA01320@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Nick Chin wrote:
>
> hello,
>
> ive been trying to solve an equation of the form
>
> tan(kx) + m tan(x) = 0 , solving for x
>
> but mathematica says " The equations appear to involve the variables to
> be solved for in an essentially non-algebraic way. "
>
> So is there another way to use mathematica to solve, or is it powerless
> for this problem?
>
> thanks
>
> Nick
For specific integer or rational values of 'k' you can solve as below.
In[2]:= InputForm[Solve[Tan[3*x]+m*Tan[x]==0, x]]
Solve::ifun: Inverse functions are being used by Solve, so some
solutions may
not be found; use Reduce for complete solution information.
Out[2]//InputForm=
{{x -> 0}, {x -> -Pi}, {x -> Pi},
{x -> -ArcCos[-(Sqrt[1 + 3*m]/Sqrt[4 + 4*m])]},
{x -> ArcCos[-(Sqrt[1 + 3*m]/Sqrt[4 + 4*m])]},
{x -> -ArcCos[Sqrt[1 + 3*m]/Sqrt[4 + 4*m]]},
{x -> ArcCos[Sqrt[1 + 3*m]/Sqrt[4 + 4*m]]}}
For generic 'k' I have no idea what you might expect as a solution set.
Daniel Lichtblau
Wolfram Research
- References:
- solved in a non algebraic way?
- From: Nick Chin <nchin@students.uiuc.edu>
- solved in a non algebraic way?