Re: NSolve unable to find all possible roots
- To: mathgroup at smc.vnet.net
- Subject: [mg115606] Re: NSolve unable to find all possible roots
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Sun, 16 Jan 2011 05:53:00 -0500 (EST)
There is only one solution:
eq = x (Sqrt[-13.319 - x^2] + 2.41*Sqrt[1.004 - x^2]) // Rationalize;
Solve[eq == 0, x]
{{x -> 0}}
(eq /. x -> # &) /@ {0, 1.99, -1.99}
{0, 0.\[VeryThinSpace]+ 16.5178 I, 0.\[VeryThinSpace]- 16.5178 I}
(Your other two "roots" are not roots.)
Perhaps you only wanted the real part to be zero? In that case, we have
infinitely many solutions (in addition to 0):
eq = Re[Sqrt[-13.319 - x^2] + 2.41*Sqrt[1.004 - x^2] // Rationalize];
Reduce[eq == 0, x]
(Re[x] <= -(Sqrt[(251/10)]/5) &&
Im[x] == 0) || (Re[x] >= Sqrt[251/10]/5 && Im[x] == 0)
Sqrt[251/10]/5 // N
1.002
Here are two of those solutions:
eq /. {{x -> -(Sqrt[(251/10)]/5)}, {x -> Sqrt[251/10]/5}}
{0, 0}
1.99 and -1.99 satisfy that version of the equation, also.
Bobby
On Sat, 15 Jan 2011 03:45:17 -0600, Luiz Melo <luiz.melo at polymtl.ca> wrote:
> Dear mathgroup,
> The equation below has three possible roots, namely: 0., 1.99, -1.99.
>
> eq = x*(Sqrt[-13.319 - x^2] + 2.41*Sqrt[1.004 - x^2])
>
> If we try NSolve[eq == 0, x], we get {{kx-> 0.}} only.
>
> How to instruct NSolve to search for the other two roots of the above
> equation?
>
> Thank you
> Luiz Melo
>
> --
>
>
--
DrMajorBob at yahoo.com