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How does Solve works ??


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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