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# Interpreting a result obtain with Reduce that includes pure function

Posted 11 years ago
 Hello,I used Reduce on a set of inequalities and I got the messageReduce::ratnz: Reduce was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result plus a result that included the following condition c < Root[19. T^3 - 30. T^2 #1 + 8. #1^3 &, 3]Does it mean that "c" must be lower than the third root of the equation 19.T^3-30.x T^2+8.x^3==0where x is the unknown? Is 19. an abbreviation for an irrational number close to 19?Thank you in advance for your help
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Posted 11 years ago
 >Does it mean that "c" must be lower than the third root of the equation Yes,  Root is aften returned in results by Solve and Reducetutorial/AlgebraicNumbers To get a sense of how the root behaves relative to T:Plot[Root[19. T^3 - 30. T^2 #1 + 8. #1^3 &, 3], {T, -5, 5}] But since this is just a third-degree polynomial you can get the roots explicitly by telling Reduce to expand cubics (similar option exists for quartics)Reduce[19 T^3 - 30 T^2 x + 8 x^3 == 0, x, Cubics->True]>Is 19. an abbreviation for an irrational number close to 19?It represents a machine-precision number tutorial/NumericalPrecision
Posted 11 years ago
 Thank you! The graph was interesting to look at S