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