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Re: How does Solve works ??
*To*: mathgroup at smc.vnet.net
*Subject*: [mg80250] Re: [mg80183] How does Solve works ??
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Wed, 15 Aug 2007 04:29:15 -0400 (EDT)
*Reply-to*: hanlonr at cox.net
The exponent in expr^(1/2) has to be in parentheses
Clear[n, k];
{n, k} /.
FullSimplify[Solve[{e1 == n^2 - k^2, e2 == 2 n*k}, {n, k}][[3]]]
{e2/(Sqrt[2]*Sqrt[Sqrt[e1^2 + e2^2] - e1]),
Sqrt[(1/2)*Sqrt[e1^2 + e2^2] - e1/2]}
FullSimplify[% == {(e1 + (e1^2 + e2^2)^(1/2))^(1/2)*Sqrt[1/2],
(-e1 + (e1^2 + e2^2)^(1/2))^(1/2)*Sqrt[1/2]}, {e1 > 0, e2 > 0}]
True
Bob Hanlon
---- Ravinder K Banyal <r.banyal at neu.edu> wrote:
> Hi,
> I am just a beginner in Mathematica.
> I have two simple equations as follows:
> e1=n^2-k^2;
> e2=2 n*k;
> If I solve for n and k, I should get
> n = (e1 + (e1^2 + e2^2)^1/2)^1/2 * sqrt(1/2)
> k = (-e1 + (e1^2 + e2^2)^1/2)^1/2 * sqrt(1/2)
> However when I use mathematica (ver 5.1) to solve the above equations I
> do not get the intended results.
> Solve[e1 -n^2+k^2 = = 0, e2-2n*k = = 0, {n,k}]
> None of the four roots generated by mathematica matches with above results.
>
> Any comment please.....
>
> Regards,
> -ravi
>
>
>
>
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