       Re: How does Solve works ??

• To: mathgroup at smc.vnet.net
• Subject: [mg80232] Re: How does Solve works ??
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 15 Aug 2007 04:19:53 -0400 (EDT)
• Organization: Uni Leipzig
• References: <f9s3j1\$abs\$1@smc.vnet.net>

```Hi,

with Mathematica 6.0, the third root of
ss = Solve[{e1 - n^2 + k^2 == 0, e2 - 2 n*k == 0}, {n, k}] //
FullSimplify[#,
e1 \[Element] Reals && e1 \[Element] Reals && e1 > 0 && e2 > 0] &

matches you result, as to see from
({n, k} /. {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]}) - # & /@ ({n, k} /. ss) //
FullSimplify[#,
e1 \[Element] Reals && e1 \[Element] Reals && e1 > 0 && e2 > 0] &

Regards
Jens

Ravinder K Banyal 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.
>
>
> Regards,
> -ravi
>
>
>
>

```

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