an equation containg radicals

*To*: mathgroup at smc.vnet.net*Subject*: [mg69648] an equation containg radicals*From*: dimmechan at yahoo.com*Date*: Tue, 19 Sep 2006 05:45:07 -0400 (EDT)

Hello to all. In a crack problem appeared the following function. K[p_] := 1 - 4*(1 - v)*Î»^2*p^2*(1 - Sqrt[e^2 - p^2]/Sqrt[a^2 - p^2]) a = 1/Î»; Here are some typical values for the involving constants consts = {e -> 1/1000, v -> 3/10, Î» -> 10^(-5)}; Here is the solution obtained with Solve sols = FullSimplify[Solve[eq = K[p] == 0, p]] {{p -> (-Sqrt[2])*Sqrt[-(1/(Î»^2*(-9 + 8*v + Sqrt[-15 + 16*v + 64*e^2*(-1 + v)^2*Î»^2])))]}, {p -> Sqrt[2]*Sqrt[-(1/(Î»^2*(-9 + 8*v + Sqrt[-15 + 16*v + 64*e^2*(-1 + v)^2*Î»^2])))]}, {p -> (-Sqrt[2])*Sqrt[1/(Î»^2*(9 - 8*v + Sqrt[-15 + 16*v + 64*e^2*(-1 + v)^2*Î»^2]))]}, {p -> Sqrt[2]*Sqrt[1/(Î»^2*(9 - 8*v + Sqrt[-15 + 16*v + 64*e^2*(-1 + v)^2*Î»^2]))]}} What I need now is to see which roots (or if all roots) are extreneous (i.e. they do not satisfy the intial equation K[p]=0). This is a difficult task for Mathematica. TimeConstrained[FullSimplify[eq /. sols], 300, "Failed"] "Failed" However replacing the values for the constants it is verified that all solutions (for this typical values of the constants) are extreneous. eq /. sols /. consts {False, False, False, False} This can be verified also by the following command Solve[eq /. consts, p] {} My question is if it a way to "help" a bit Mathematica in the above verification with the symbolic parameters. Thanks in advance for any help.

**Follow-Ups**:**Re: an equation containg radicals***From:*Daniel Lichtblau <danl@wolfram.com>