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Beware of NSolve


Run v. 4.2 on Mac:

f=5/432 - 11/(27*Sqrt[70]*Sqrt[19 - 1890*x]) + x/(2*Sqrt[38/35 - 108*x]);

 Solve[f==0,x]  returns 2 real roots:

{{x -> (-171 - 25*Sqrt[105])/30240}, {x -> (-171 + 25*Sqrt[105])/30240}}

NSolve[f==0,x]  returns 4 real roots:

{{x -> -0.10481082961146104}, {x -> -0.014126116704662378}, 
 {x -> 0.002816592895138556}, {x -> 0.0003796126802330315}}

Roots 1 and 4 are incorrect.  (Just plot f)

Had a similar problem with a quartic 3 months ago.  This is a
simpler example.


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