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 > > > >