XPost: sci.math   
   From: ivgroups@onlinehome.de   
      
   "Richard Fateman" wrote in news:mp3tjb$n6q$1@speranza.aioe.org...   
   >> The partial question of this thread is: Which general kinds of radical   
   >> equations (with no nested radicals) are solvable symbolically?   
   > You will have to define your terms.  "radical equation".   
   > "solve"   
   > "solve symbolically"   
   Algebraic expression: Wikipedia: Algebraic expression   
   Radical equation: An equation of one variable that consists only of   
   algebraic expressions and contains at least one radical of an expression   
   that contains the variable.   
   In a first stage, we can consider only radical equations that don't contain   
   nested radicals.   
   Symbolic solutions: Some of the solutions are a symbolic solution.   
   A symbolic solution: There is an algebraic expression only for this   
   solution.   
   Solving symbolically: Finding the symbolic solutions of the equation   
      
   > A college course in abstract algebra   or "modern algebra"   
   > (this is not high school algebra)   
   > might answer all your questions.   
   > Without such a background it may be difficult to explain   
   > the answer to you.   
   Because you have visited such courses, you could try to answer my question.   
   My impression is: The algebra of equations (no differential equations, no   
   differential equations, no integro differential equations) treats only   
   polynomial equations and rational equations.   
      
   I assume, each radical equation has only algebraic solutions.   
      
   Is there a general method to transform each given radical equation into its   
   corresponding polynomial equation?   
      
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